Determine if True log base 4 of 64=3

Problem

(log_4)(64)=3

Solution

1. Identify the logarithmic equation and its components, where the base is 4 the argument is 64 and the exponent is 3

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

3. Substitute the values into the exponential form to get 4=64

4. Calculate the value of the exponential expression 4 by multiplying 4⋅4⋅4

5. Compare the result of the calculation to the argument of the logarithm to determine if the statement is true.

6. Verify that 4⋅4=16 and 16⋅4=64

Final Answer

(log_4)(64)=3* is True

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