Question

log 128 to the base 8
a)7/3 b)16 c)3/7 d)1/16

Answer 1

Log8128=Log(128) ÷ Log(8)

Log(128)= 2.10720996965

Log(8)=0.903089986992

Log8128=2.10720996965 ÷ 0.903089986992

Ans=2.33333333333

It means 1 option is right

Answer 2

Given,

$\log_8 128$

We have to find, the value of $\log_8 128$ is:

Solution:

∴ $\log_8 128$

= $\log_8 (64\times 2)$

Using the logarithm identity:

$\log (a\times b)$ = $\log a$ + $\log b$

= $\log_8 64+\log_8 2$

= $\log_8 8^2+\log_{2^3} 2$

Using the logarithm identity:

$\log a^b$ = b$\log a$ and

$\log_{a^c} a$ = $\dfrac{1}{c} \log_aa$

= $2\log_8 8+\dfrac{1}{3} \log_{2} 2$

= 2 + $\dfrac{1}{3}$ [ ∵ $\log_{a} a$ = 1]

= $\dfrac{6+1}{3}$

= $\dfrac{7}{3}$

∴ $\log_8 128$ = $\dfrac{7}{3}$

Thus, the required "option a) $\dfrac{7}{3}$" is correct.