Question

Find the value of log 8 base root 2​

Answer 1

Answer:

6

Step-by-step explanation:

log of any value is power to which the base has to be increased to get that value

hence,

$log_{\sqrt{2}} 8 =$ the power to which $\sqrt{2}$ has to be raised to get the value "8"

$\sqrt{2} ^{n} = 2^{3}$

Squaring both sides,

$2^{n} = 2^{6}\\ n=6$

Answer 2

The value for the given logarithmic expression is 6.

Step-by-step explanation:

The given expression is

$\log_{\sqrt2}8$

We can write 8 in exponent form as $8=2^3$

Thus, the given expression becomes

$\log_{\sqrt2}(2^3)$

We can rewrite $2=(\sqrt2)^2$

Thus, we have

$\log_{\sqrt2}((\sqrt2)^2)^3)\\\\log_{\sqrt2}((\sqrt2))^6$

Using the logarithmic property $\log_m m^y=y$

$\log_{\sqrt2}((\sqrt2))^6=6$

#Learn More:

Solve this logarithm equation

https://brainly.in/question/3544539