Question

determine the correspondence between each logarithmic equation and its appropriate solution method. The logarithmic equations are log3(x)=2, log3(x+1) =log3(5), log4(10) =x. The appropriate solution methods are Apply the change of base formula to find an approximate answer, set the expression inside the logarithms equal to each other, transform the equation to exponential form to solve it.

Answer 1

Matches:

- log3(x) = 2 → Transform to exponential form. x = 3^2 = 9.

- log3(x+1) = log3(5) → Set the expressions inside the logs equal. x + 1 = 5 ⇒ x = 4.

- log4(10) = x → Apply the change-of-base formula to get an approximate value. x = ln(10)/ln(4) ≈ 1.660964.