Questions: Write the equation in its equivalent exponential form. Then solve for x. log2(x-5) = 3

Solution Steps

To convert the logarithmic equation to its equivalent exponential form, we use the property that \(\log_b(a) = c\) is equivalent to \(b^c = a\). Then, solve for \(x\) by isolating it on one side of the equation.

1. Convert the logarithmic equation \(\log_{2}(x-5) = 3\) to its exponential form.
2. Solve the resulting exponential equation for \(x\).

Starting with the logarithmic equation: \[ \log_{2}(x - 5) = 3 \] we convert it to its equivalent exponential form: \[ 2^3 = x - 5 \]

Calculating \(2^3\) gives us: \[ 8 = x - 5 \]

To isolate \(x\), we add \(5\) to both sides: \[ x = 8 + 5 \] which simplifies to: \[ x = 13 \]

Final Answer