Question

log8[log2{log3(4x+17)}]=1/3

Answer 1

Answer:

The value of x is 16.

Step-by-step explanation:

The given expression is

$log_8[log_2\{log_3(4x+17)\}]=\frac{1}{3}$

According to property of logarithm

$log_ab=x\Rightarrow b=a^x$            ....(1)

Using the  property of logarithm, we get

$log_2\{log_3(4x+17)\}=8^{\frac{1}{3}}$

$log_2\{log_3(4x+17)\}=2$

$log_3(4x+17)=2^2$                     [using (1)]

$log_3(4x+17)=4$

$4x+17=3^4$                                [using (1)]

$4x+17=81$

Subtract 17 from both sides.

$4x=64$

Divide both sides by 4.

$x=16$

Therefore the value of x is 16.