Exponential Functios questions help?

**skg94** · November 13th 2012, 06:58 PM

1.
3^(x-2)=5^x
2^(x-2)=3^(x+1)

cant use log.

2. Lucas is hoping to take a vacation after he finishes university. To do this he needs $5000, he finishes with $3500 in an investment that pays 8.4 per year, compounded quarterly. how long will Lucas have to wait before he has enough money to go on vacation.

I did 3500*1.084^x/4 wrong results

**Prove It** · November 13th 2012, 07:47 PM

You can't solve either of question 1 without logarithms.

**Soroban** · November 13th 2012, 07:53 PM

Hello, skg94!

$1(a)\;3^{x-2}\:=\:5^x$
. $(b)\;2^{x-2}\:=\:3^{x+1}$

Can't use log. . Then they can't be solved.

2. Lucas is hoping to take a vacation after he finishes university. .To do this he needs $5000.
He has $3500 in an investment that pays 8.4% per year, compounded quarterly.
How long will Lucas have to wait before he has enough money to go on vacation?

The formula is: . $A \;=\;P(1 + i)^n$

. . where: . $\begin{Bmatrix} P &=& \text{principal invested} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$

We have: . $P = 3500,\;i = \frac{0.084}{4} = 0.021,\;n = 4x$
. . where $x$ is the number of years.

Then: . $3500(1.021)^{4x} \:=\:5000 \quad\Rightarrow\quad (1.021)^{4x} \:=\:\tfrac{10}{7}$

Take logs: . $\ln(1.021)^{4x} \:=\:\ln\left(\tfrac{10}{7}\right) \quad\Rightarrow\quad 4x\ln(1.021) \:=\:\ln\left(\tfrac{10}{7}\right)$

Therefore: . $x \;=\;\frac{\ln(\frac{10}{7})}{4\ln(1.021)} \;\approx\;4.29\text{ years}$

**skg94** · November 13th 2012, 08:00 PM

my answer says its 4.5

its nice to know the interest formula though, if i were to graph it which formula would i use?

3500(1+(.084/4)^4x ?
or 3500 * (1.021)^4x

well the thing is while i know how to do log, my test tomorrow will strictly be using expontential fuctions only, so i guess my teacher made a mistake in this review

**Prove It** · November 13th 2012, 08:02 PM

Why would you think that a test on exponential functions wouldn't include logarithms? Logarithms are the inverse functions of exponentials, and so MUST be used in many cases involving exponential functions, such as the ones above.

**skg94** · November 13th 2012, 08:22 PM

Because the the teacher hasnt taught it so i cant be tested on something i havent been taught?
If he gives a test on lessons he hasnt even mentioned then how can i be expected to answer them.
I know log because i was told to do this using log, but seeing as how i wouldnt be able to use them on a quiz where i havent learned logs i decided to ask if there is a way without them, which there isnt

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