Evaluate log base 128 of 2

Problem

(log_128)(2)

Solution

1. Identify the logarithmic expression and set it equal to a variable x

(log_128)(2)=x

2. Rewrite the logarithmic equation in its equivalent exponential form.

128=2

3. Express the base 128 as a power of 2 to create common bases.

(2)x=2

4. Apply the power of a power rule for exponents on the left side.

2(7*x)=2

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

7*x=1

6. Solve for x by dividing both sides by 7.

x=1/7

Final Answer

(log_128)(2)=1/7

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