Solving Exponential and Logarithmic Equations Answers

What are the potential solutions to the equation below?

What common base can be used to rewrite each side of the equation

Carlene is saving her money to buy a $500 desk. She deposits $400 into an account with an annual interest rate of 6% compounded continuously. The equation represents the situation, where t is the number of years the money needs to remain in the account. About how long must Carlene wait to have enough money to buy the desk? Use a calculator and round your answer to the nearest whole number.