Question

please answer full anwer not only answer​

Answer 1

$\large\underline{\sf{Given- }}$

$\rm :\longmapsto\:log( {x}^{2} - 44) = 2$

$\large\underline{\sf{To\:Find - }}$

The value of x

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:log( {x}^{2} - 44) = 2$

can be rewritten as

$\rm :\longmapsto\:log( {x}^{2} - 44) = 2 \times 1$

We know,

$\boxed{ \bf{ \: log10 = 1}}$

So, using this identity, we get

$\rm :\longmapsto\:log {(x}^{2} - 44) = 2log10$

We know,

$\boxed{ \bf{ \: log {x}^{y} = y \: logx}}$

$\rm :\longmapsto\:log {(x}^{2} - 44) = log {10}^{2}$

$\rm :\longmapsto\: {x}^{2} - 44 = 100$

$\rm :\longmapsto\: {x}^{2} = 100 + 44$

$\rm :\longmapsto\: {x}^{2} = 144$

$\rm :\longmapsto\: {x}^{2} = {12}^{2}$

$\bf\implies \:x \: = \: \pm \: 12$

Verification :-

Given equation is

$\rm :\longmapsto\:log( {x}^{2} - 44) = 2$

Case - 1 When x = 12

$\rm :\longmapsto\:log( {12}^{2} - 44) = 2$

$\rm :\longmapsto\:log(144 - 44) = 2$

$\rm :\longmapsto\:log(100) = 2$

$\rm :\longmapsto\:log( {10}^{2} ) = 2$

$\rm :\longmapsto\:2log( {10}^{} ) = 2$

$\rm :\longmapsto\:2 = 2$

Hence, Verified

Case - 2 When x = - 12

$\rm :\longmapsto\:log( {( - 12)}^{2} - 44) = 2$

$\rm :\longmapsto\:log(144 - 44) = 2$

$\rm :\longmapsto\:log(100) = 2$

$\rm :\longmapsto\:log(10) {}^{2} = 2$

$\rm :\longmapsto\:2log(10) {}^{} = 2$

$\rm :\longmapsto\:2 = 2$

Hence, Verified

Additional Information :-

$\boxed{ \bf{ \: log(xy) = logx \: + \: logy}}$

$\boxed{ \bf{ \: log(x \div y) = logx \: - \: logy}}$

$\boxed{ \bf{ \: log {x}^{y} = y \: logx}}$

$\boxed{ \bf{ \: log_{x}(x) = 1}}$

$\boxed{ \bf{ \: log_{x}(y) = \frac{logy}{logx} }}$

$\boxed{ \bf{ \: log_{ {x}^{y} }( {x}^{z} ) = \frac{z}{y}}}$

$\boxed{ \bf{ \: {e}^{logx} = x}}$

$\boxed{ \bf{ \: {e}^{ylogx} = {x}^{y} }}$

$\boxed{ \bf{ \: {a}^{ log_{a}(x) } = x}}$

Answer 2

\large\underline{\sf{To\:Find - }}

ToFind−

The value of x

\large\underline{\sf{Solution-}}

Solution−

Given that

\rm :\longmapsto\:log( {x}^{2} - 44) = 2:⟼log(x

2

−44)=2

can be rewritten as

\rm :\longmapsto\:log( {x}^{2} - 44) = 2 \times 1:⟼log(x

2

−44)=2×1

We know,

\boxed{ \bf{ \: log10 = 1}}

$\large\underline{\sf{Given- }}$

log10=1

So, using this identity, we get

\rm :\longmapsto\:log {(x}^{2} - 44) = 2log10:⟼log(x

2

−44)=2log10

We know,

\boxed{ \bf{ \: log {x}^{y} = y \: logx}}

logx

y

=ylogx

\rm :\longmapsto\:log {(x}^{2} - 44) = log {10}^{2} :⟼log(x

2

−44)=log10

2

\rm :\longmapsto\: {x}^{2} - 44 = 100:⟼x

2

−44=100

\rm :\longmapsto\: {x}^{2} = 100 + 44:⟼x

2

=100+44

\rm :\longmapsto\: {x}^{2} = 144:⟼x

2

=144

\rm :\longmapsto\: {x}^{2} = {12}^{2} :⟼x

2

=12

2

\bf\implies \:x \: = \: \pm \: 12⟹x=±12

Verification :-

Given equation is

\rm :\longmapsto\:log( {x}^{2} - 44) = 2:⟼log(x

2

−44)=2

Case - 1 When x = 12

\rm :\longmapsto\:log( {12}^{2} - 44) = 2:⟼log(12

2

−44)=2

\rm :\longmapsto\:log(144 - 44) = 2:⟼log(144−44)=2

\rm :\longmapsto\:log(100) = 2:⟼log(100)=2

\rm :\longmapsto\:log( {10}^{2} ) = 2:⟼log(10

2

)=2

\rm :\longmapsto\:2log( {10}^{} ) = 2:⟼2log(10

)=2

\rm :\longmapsto\:2 = 2:⟼2=2

Hence, Verified

Case - 2 When x = - 12

\rm :\longmapsto\:log( {( - 12)}^{2} - 44) = 2:⟼log((−12)

2

−44)=2

\rm :\longmapsto\:log(144 - 44) = 2:⟼log(144−44)=2

\rm :\longmapsto\:log(100) = 2:⟼log(100)=2

\rm :\longmapsto\:log(10) {}^{2} = 2:⟼log(10)

2

=2

\rm :\longmapsto\:2log(10) {}^{} = 2:⟼2log(10)

=2

\rm :\longmapsto\:2 = 2:⟼2=2

Hence, Verified

Additional Information :-

\boxed{ \bf{ \: log(xy) = logx \: + \: logy}}

log(xy)=logx+logy

\boxed{ \bf{ \: log(x \div y) = logx \: - \: logy}}

log(x÷y)=logx−logy

\boxed{ \bf{ \: log {x}^{y} = y \: logx}}

logx

y

=ylogx

\boxed{ \bf{ \: log_{x}(x) = 1}}

log

x

(x)=1

\boxed{ \bf{ \: log_{x}(y) = \frac{logy}{logx} }}

log

x

(y)=

logx

logy

\boxed{ \bf{ \: log_{ {x}^{y} }( {x}^{z} ) = \frac{z}{y}}}

log

x

y

(x

z

)=

y

z

\boxed{ \bf{ \: {e}^{logx} = x}}

e

logx

=x

\boxed{ \bf{ \: {e}^{ylogx} = {x}^{y} }}

e

ylogx

=x

y

\boxed{ \bf{ \: {a}^{ log_{a}(x) } = x}}

a

log

a

(x)

=x

Step-by-step explanation:

$\large\underline{\sf{Given- }}Given−</h2><h2></h2><h2>\rm :\longmapsto\:log( {x}^{2} - 44) = 2:⟼log(x2−44)=2</h2><h2></h2><h2>\large\underline{\sf{To\:Find - }}ToFind−</h2><h2></h2><h2>The value of x</h2><h2></h2><h2>\large\underline{\sf{Solution-}}Solution−</h2><h2></h2><h2>Given that</h2><h2></h2><h2>\rm :\longmapsto\:log( {x}^{2} - 44) = 2:⟼log(x2−44)=2</h2><h2></h2><h2>can be rewritten as</h2><h2></h2><h2>\rm :\longmapsto\:log( {x}^{2} - 44) = 2 \times 1:⟼log(x2−44)=2×1</h2><h2></h2><h2>We know,</h2><h2></h2><h2>\boxed{ \bf{ \: log10 = 1}}log10=1</h2><h2></h2><h2>So, using this identity, we get</h2><h2></h2><h2>\rm :\longmapsto\:log {(x}^{2} - 44) = 2log10:⟼log(x2−44)=2log10</h2><h2></h2><h2>We know,</h2><h2></h2><h2>\boxed{ \bf{ \: log {x}^{y} = y \: logx}}logxy=ylogx</h2><h2></h2><h2>\rm :\longmapsto\:log {(x}^{2} - 44) = log {10}^{2}:⟼log(x2−44)=log102</h2><h2></h2><h2>\rm :\longmapsto\: {x}^{2} - 44 = 100:⟼x2−44=100</h2><h2></h2><h2>\rm :\longmapsto\: {x}^{2} = 100 + 44:⟼x2=100+44</h2><h2></h2><h2>\rm :\longmapsto\: {x}^{2} = 144:⟼x2=144</h2><h2></h2><h2>\rm :\longmapsto\: {x}^{2} = {12}^{2}:⟼x2=122</h2><h2></h2><h2>\bf\implies \:x \: = \: \pm \: 12⟹x=±12</h2><h2></h2><h2>Verification :-</h2><h2></h2><h2>Given equation is</h2><h2></h2><h2>\rm :\longmapsto\:log( {x}^{2} - 44) = 2:⟼log(x2−44)=2</h2><h2></h2><h2>Case - 1 When x = 12</h2><h2></h2><h2>\rm :\longmapsto\:log( {12}^{2} - 44) = 2:⟼log(122−44)=2</h2><h2></h2><h2>\rm :\longmapsto\:log(144 - 44) = 2:⟼log(144−44)=2</h2><h2></h2><h2>\rm :\longmapsto\:log(100) = 2:⟼log(100)=2</h2><h2></h2><h2>\rm :\longmapsto\:log( {10}^{2} ) = 2:⟼log(102)=2</h2><h2></h2><h2>\rm :\longmapsto\:2log( {10}^{} ) = 2:⟼2log(10)=2</h2><h2></h2><h2>\rm :\longmapsto\:2 = 2:⟼2=2</h2><h2></h2><h2>Hence, Verified</h2><h2></h2><h2>Case - 2 When x = - 12</h2><h2></h2><h2>\rm :\longmapsto\:log( {( - 12)}^{2} - 44) = 2:⟼log((−12)2−44)=2</h2><h2></h2><h2>\rm :\longmapsto\:log(144 - 44) = 2:⟼log(144−44)=2</h2><h2></h2><h2>\rm :\longmapsto\:log(100) = 2:⟼log(100)=2</h2><h2></h2><h2>\rm :\longmapsto\:log(10) {}^{2} = 2:⟼log(10)2=2</h2><h2></h2><h2>\rm :\longmapsto\:2log(10) {}^{} = 2:⟼2log(10)=2</h2><h2></h2><h2>\rm :\longmapsto\:2 = 2:⟼2=2</h2><h2></h2><h2>Hence, Verified</h2><h2></h2><h2>Additional Information :-</h2><h2></h2><h2>\boxed{ \bf{ \: log(xy) = logx \: + \: logy}}log(xy)=logx+logy</h2><h2></h2><h2>\boxed{ \bf{ \: log(x \div y) = logx \: - \: logy}}log(x÷y)=logx−logy</h2><h2></h2><h2>\boxed{ \bf{ \: log {x}^{y} = y \: logx}}logxy=ylogx</h2><h2></h2><h2>\boxed{ \bf{ \: log_{x}(x) = 1}}logx(x)=1</h2><h2></h2><h2>\boxed{ \bf{ \: log_{x}(y) = \frac{logy}{logx} }}logx(y)=logxlogy</h2><h2></h2><h2>\boxed{ \bf{ \: log_{ {x}^{y} }( {x}^{z} ) = \frac{z}{y}}}logxy(xz)=yz</h2><h2></h2><h2>\boxed{ \bf{ \: {e}^{logx} = x}}elogx=x</h2><h2></h2><h2>\boxed{ \bf{ \: {e}^{ylogx} = {x}^{y} }}eylogx=xy</h2><h2></h2><h2>\boxed{ \bf{ \: {a}^{ log_{a}(x) } = x}}aloga(x)=x</h2><h2></h2><h2>$