Solving Logarithmic Equations by Converting to Exponential Form
To solve the logarithmic equation \(\log(2x + 4) = 2\), we can rewrite the equation in its exponential form. The base of the logarithm is 10 by default when no base is specified. With this in mind, the equation becomes:
\(10^{\log(2x + 4)} = 10^2\)
Since \(10^{\log(x)} = x\), we have:
\(2x + 4 = 10^2\)
\(2x + 4 = 100\)
Next, we solve for \(x\) by isolating the variable:
\(2x = 100 - 4\)
\(2x = 96\)
Divide both sides by 2 to find \(x\):
\(x = \frac{96}{2}\)
\(x = 48\)
Hence, the solution to the equation \(\log(2x + 4) = 2\) is \(x = 48\).
