Question

solve for x

1. 4 (2)^x = 64

4(2)^x = 64

Explanation:

Step1: Divide both sides by 4

Divide the equation \(4(2)^x = 64\) by 4. So we get \(\frac{4(2)^x}{4}=\frac{64}{4}\), which simplifies to \(2^x = 16\).

Step2: Express 16 as a power of 2

We know that \(16 = 2^4\). So the equation becomes \(2^x = 2^4\).

Step3: Equate the exponents

Since the bases are the same (both are 2) and the exponential function is one - to - one, we can set the exponents equal to each other. So \(x = 4\).

Answer:

\(x = 4\)