Video Transcript
Use a calculator to find the value of 𝑥 for which two-thirds to the power of 𝑥 is equal to 1.7602. Give your answer correct to two decimal places.
We begin by noticing that our equation is written in the form 𝑎 to the power of 𝑥 is equal to 𝑏. Since a logarithmic function is the inverse of an exponential function, we know that if 𝑎 to the power of 𝑥 equals 𝑏, then 𝑥 is equal to log base 𝑎 of 𝑏. The exponential equation in this question can be rewritten as the logarithmic equation 𝑥 is equal to log base two-thirds of 1.7602. Typing the right-hand side into our calculator, we get negative 1.394515 and so on.
We are asked to round this correct to two decimal places. As the four in the thousandths column is less than five, we round to negative 1.39. If two-thirds to the power of 𝑥 is equal to 1.7602, then 𝑥 is equal to negative 1.39 to two decimal places.
