Question

Solve the equation. Write the solution set with exact values given in terms of common or natural logarithms.

Answer 1

We have to solve for y:

`\begin{gathered} 1282=23^y+2 \\ 23^y=1282-2 \\ 23^y=1280 \\ \log_(23)(23^y)=\log_(23)(1280) \\ y=\log_(23)(1280) \end{gathered}`

We can express the solution in terms of a logarithm with base 23 as y = log₂₃(1280).

The approximated value is:

`y=\log_(23)(1280)\approx2.2818`

Answer:

Exact solution: y = log₂₃(1280)

Approximate solution: y ≈ 2.2818