Question

1/64)^2b = 16. To turn it into a log equation and solve, which of the following equations is correct?

A) log(1/64)^(2b) = log(16)
B) 2b * log(1/64) = log(16)
C) 2b * log(1/64) = 1/log(16)
D) 2b * log(1/64) = 16

Answer 1

The correct logarithmic form of the equation (1/64)^{2b} = 16 is 2b * log(1/64) = log(16), which corresponds to option B from the given choices.

Step-by-step explanation:

To solve the equation (1/64)^{2b} = 16 and turn it into a logarithmic equation, we can apply the logarithm on both sides of the equation, which yields the equation 2b * log(1/64) = log(16). Given the options, the correct logarithmic form to represent the given equation is option B) 2b * log(1/64) = log(16). To solve for b, we would then divide both sides by log(1/64), which simplifies the equation to b = log(16) / (2 * log(1/64)).