Question

Find x !!!

$\log _2\left(x+1\right)=\log _3\left(27\right)$

answer should be correct

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\bf{Solve\:\:for\:\:x\:\::\log _2\left(x+1\right)=\log _3\left(27\right)}$

♣ ᴀɴꜱᴡᴇʀ :

$\bf{\log _2\left(x+1\right)=\log _3\left(27\right)}$

$\log _2\left(x+1\right)=3$

$\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c$

$\log _2\left(x+1\right)=3\quad \Rightarrow \quad \:x+1=2^3$

$x+1=2^3$

$x+1=8$

$\huge\boxed{\bf{x=7}}$

Answer 2

Rewrite as an equation.

log

3

(

27

)

=

x

Rewrite  

log

3

(

27

)

=

x

in exponential form using the definition of a logarithm. If  

x

and  

b

are positive real numbers and  

b

does not equal  

1

, then  

log

b

(

x

)

=

y

is equivalent to  

b

y

=

x

.

3

x

=

27

Create equivalent expressions in the equation that all have equal bases.

3

x

=

3

3

Since the bases are the same, the two expressions are only equal if the exponents are also equal.

x

=

3