Evaluate log base 8 of 2

Problem

(log_8)(2)

Solution

1. Identify the logarithmic expression as an equation where x is the value we want to find.

(log_8)(2)=x

2. Rewrite the logarithmic equation in its equivalent exponential form using the definition by=x⇔(log_b)(x)=y

8=2

3. Express the base 8 as a power of 2 to create a common base on both sides of the equation.

(2)x=2

4. Apply the power of a power rule (am)n=a(m*n) to simplify the left side.

2(3*x)=2

5. Equate the exponents since the bases are now identical.

3*x=1

6. Solve for x by dividing both sides by 3

x=1/3

Final Answer

(log_8)(2)=1/3

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