Question

Evaluate the log without a calculator ( Show your work )

Look at image. That is the problem.

Answer 1

Answer:

8

Step-by-step explanation:

Given in the question a logarithm expression

$125^(log_{5}2)$

We will use Exponent of Log Rule

$b^(log_{b}k) = k$

here b = 5

         k = 2

Suppose

$125^(log_{5}2) = x$

take cube root on both sides of this equation

$\sqrt[ 3]{(125^(log_{5}2)}=\sqrt[3]{x}$

$\sqrt[3]{(125)} ^(log_{5}2)=\sqrt[3]{x}$

$5^(log_{5}2)}=\sqrt[3]{x}$

Now according to the rule

2 = ∛x

to remove cube root take cube on both side

x = 8

so $125^(log_{5}2 )$ = 8