b. \( \quad \log (2 x+3)=2 \)

To solve the equation \( \log(2x + 3) = 2 \), we can first rewrite the logarithmic equation in its exponential form. This means we convert it to \( 2x + 3 = 10^2 \) (since the base of the logarithm is 10). So we have: \[ 2x + 3 = 100 \] Now, subtract 3 from both sides: \[ 2x = 100 - 3 \] \[ 2x = 97 \] Next, divide both sides by 2 to isolate \( x \): \[ x = \frac{97}{2} \] This simplifies to: \[ x = 48.5 \] So the solution to the equation \( \log(2x + 3) = 2 \) is \( x = 48.5 \).