Question

solve for z.
10² = 100,000,000
z =
submit

Explanation:

Step1: Rewrite 100,000,000 as a power of 10

We know that \(100,000,000 = 10^{8}\) because \(10\times10\times10\times10\times10\times10\times10\times10 = 10^{8}\).

Step2: Set the exponents equal

Given the equation \(10^{z}=10^{8}\), since the bases are the same (both are 10) and the exponential function \(y = 10^{x}\) is one - to - one (if \(10^{a}=10^{b}\), then \(a = b\)), we can conclude that \(z = 8\).

Answer:

\(z = 8\)