Question

by converting to exponential form, find the value of the following.
log8 32

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Answer 1

Answer:

(8)^x=32

((2)^3)^x=(2)^5

3x= 5

x= 5÷3

Step-by-step explanation:

I hope it will be helpful for you

Answer 2

The value of x = $\dfrac{5}{3}$

Step-by-step explanation:

Let x = $\log_8 {32}$

To find, the value of $\log_8 {32}$ = ?

∴ x = $\log_8 {32}$

⇒ x = $\log_{2^3} {32}$

⇒ x = $\dfrac{1}{3} \log_{2} {32}$ [ Using logarithm properties]

⇒ x = $\dfrac{1}{3} \log_{2} {2^5}$

⇒ x = $\dfrac{5}{3} \log_{2} {2}$

Using the logarithm identity,

$\log{a^m}=m\log a$

⇒ x = $\dfrac{5}{3} \times 1$

Using the logarithm identity,

$\log_{a} {a}$ = 1

⇒ x = $\dfrac{5}{3}$

Thus, the value of x = $\dfrac{5}{3}$