Question

How do you solve for t in this exponential equation? 100,000=8,970(1+0.0469)^t

Answer 1

1. Combine 1+0.0469 to obtain 1.0469: \[100000=8970(1.0469)^t\]
2. take the log (either the natural log or the common log) of both sides.
Note that on the right side you have both exponentiation and multiplication.

Can you now solve this problem (that is, can you now solve for t)? If not, what further help do you need to solve it?

Answer 2

After I combine I need to take the log of each side. So the first side would be 5 but how do you get a log for the second half of the equation?

Answer 3

Because you got a '5' from the left side of the equation, I see you're using common logs (not natural logs). This is fine.

What do you remember about rules of logs?

log a*b = log a + log b

There are two more such rules. What are they?

Hint: you might want to look up "rules of logs."

Answer 4

log a/b = log a - log b is one
and c log b = log b^c

Answer 5

Nice work.

So, if \[y=a*b^2\] take the common log of both sides. You'll need to use two of the three rules of logs that we've listed.

Answer 6

I am still unsure how to take a log of the second half of the equation. To I take the log of each part such as 8,970 and 1.069^t?

Answer 7

*DO

Answer 8

I was hoping that the simpler example\[y=a*b^2\] would be easier to manage.

Try this: find the common log of both sides of

1) y = a * b

2) z = b^2

for practice. Then we'll address your actual problem.

Answer 9

In each case, just choose the appropriate rule of logs from the three we've listed.

Answer 10

Note that ' * ' signifies multiplication here.

Answer 11

Sorry if this is hard for you. I have faith that you can solve the given problem. But OpenStudy says you are "just looking around." If at all possible, please stick with the problem solution until you and your helper arrive at the answer you need.

Answer 12

\(\bf 100,000=8,970(1+0.0469)^t\implies \cfrac{100,000}{8,970}=(1+0.0469)^t
\\ \quad \\
\textit{log cancellation rule of }log_{\color{blue}{ a}}{\color{blue}{ a}}^x=x\qquad thus
\\ \quad \\
log_{(1+0.0469)}\left(\frac{100,000}{8,970}\right)=log_{{\color{brown}{ (1+0.0469)}}}\left[{\color{brown}{ (1+0.0469)}}\right]^t
\\ \quad \\
log_{(1+0.0469)}\left(\frac{100,000}{8,970}\right)=t\)

Answer 13

This student (dizzyizzybelle) is currently offline.

Answer 14

no real sense in playing with any base other than the natural one ....