Question

solve the equation log4x+log4(x-6)=2

Answer 1

We know the property,
logA + logB = logAB

So, by this ...

log4x + log4(x-6) = 2
log[(4x)4(x-6)] = 2

2 can be written as log10 + log10 => log100

Now,

log[ 16x^2 - 96x ] = log100
16x^2 - 96x = 100
4x^2 - 24x - 25 = 0
value of x solved in the pic ...

...plz tell me if the solution is wrong , I will try again..



《●☆☆☆hope it helps you☆☆☆●》

Answer 2

$\huge\sf\pink{Answer}$

☞ Your answer is 8

$\rule{110}1$

$\huge\sf\blue{Given}$

➝ $\sf log_{4}(x) + log_{4}(x - 6) = 2$

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

✭ Value of 'x' = ?

$\rule{110}1$

$\huge\sf\purple{Steps}$

• Using property :

$\longrightarrow \: \large { \boxed { \sf{ log_{e}(a) + log_{e}(b) = log_{e}(a.b) }}}$

• So that :

$\leadsto \: { \sf{ log_{4}(x(x - 6) ) = 2 }}$

$\leadsto{ \sf{ log_{4}(x {}^{2} - 6x) = 2 }}$

• Using property :

$\longrightarrow \: \large { \sf { if \: \: log_{e}(a) = b \: \: then \: \: { \boxed{ \sf{ a = {e}^{b}}}} }}$

• So that :

$\twoheadrightarrow \: { \sf{ (x {}^{2} - 6x) = {(4)}^{2} }}$

$\twoheadrightarrow \: { \sf{ (x {}^{2} - 6x) = 16 }}$

$\twoheadrightarrow \: { \sf{ x {}^{2} - 6x - 16 = 0 }}$

$\twoheadrightarrow \: { \sf{ x {}^{2} - 8x + 2x- 16 = 0 }}$

$\twoheadrightarrow \: { \sf {x (x- 8) + 2(x- 8) = 0 }}$

$\twoheadrightarrow \: { \sf{ (x + 2)(x- 8) = 0 }}$

$\large \: \red { \twoheadrightarrow{ \sf{ x = - 2 \: \:, \: \: 8}}}$

• But x > 0 , So ...

$\orange { \dashrightarrow{ \sf{ x = 8}}}$

$\rule{170}3$