Question

10000 = 4000(1.04)^t
Solve for t.

Answer 1

\[\begin{align*}
10000&=4000(1.04)^t\\\\
\frac{10000}{4000}&=\frac{4000}{4000}(1.04)^t\\\\
\frac{10}{4}&=(1.04)^t\\\\
\log_{1.04}\frac{10}{4}&=\log_{1.04}(1.04)^t\\\\
\log_{1.04}\frac{10}{4}&=t\log_{1.04}1.04\\\\
\log_{1.04}\frac{10}{4}&=t
\end{align*}\]

Answer 2

Use the change of base formula:
\[\large \log_ba=\frac{\ln a}{\ln b}\]

Answer 3

To be fair, I already have shown you how to get the answer. It's a matter of using a calculator now.

http://www.wolframalpha.com/input/?i=ln%2810%2F4%29%2Fln%281.04%29

Answer 4

\(\Large \bf {
{\color{blue}{ b}}={\color{brown}{ a}}^y\implies log_{\color{brown}{ a}}{\color{blue}{ b}}=y\qquad thus
\\ \quad \\
{\color{blue}{ 10000}} = {\color{brown}{4000(1.04)}}^t\implies ? }\)

Answer 5

;)