Question

Rewrite 2x = 128 as a logarithmic equation.

a. logx128 = 2
b. log2x = 128
c. log2128 = x
d. log128x = 2

Answer 1

The logarithmic equation equivalent to 2x = 128 is c) log2128 = x.

Step-by-step explanation:

The logarithmic equation equivalent to 2x = 128 is option c. log2128 = x.

To rewrite the equation as a logarithmic equation, we need to remember that logarithms are the inverse operations of exponentiation.

So, in the equation 2x = 128, we can express the left side (2x) as an exponent using the base 2. This gives us 2^x = 128.

Now, we can rewrite the equation using logarithms. Taking the logarithm base 2 of both sides, we have log2(2^x) = log2(128).

Applying the exponent rule for logarithms, which states that loga(b^c) = c * loga(b), we simplify the equation to x * log2(2) = log2(128).

Since log2(2) = 1, the equation further simplifies to x = log2(128). Hence, the correct logarithmic equation is log2128 = x.