Exponential Equation

• Sep 25th 2009, 02:03 PM
katekate
Exponential Equation
3^(3x+5) = 5

Thgis is precalc review for my calc class... I think I have to take the log of both sides and then the exponent goes out front or something like that but I'm stuck.
• Sep 25th 2009, 02:37 PM
pickslides
$\displaystyle 3^{3x+5} = 5$

using $\displaystyle a^b= c \Rightarrow b = \log_ac$

then

$\displaystyle 3x+5 = \log_35$

Can you solve it from here?
• Sep 25th 2009, 02:43 PM
katekate
Yes, but only with a calculator and converting to decimals. I don't really have the theory down.
• Sep 25th 2009, 03:35 PM
skeeter
Quote:

Originally Posted by katekate
3^(3x+5) = 5

Thgis is precalc review for my calc class... I think I have to take the log of both sides and then the exponent goes out front or something like that but I'm stuck.

$\displaystyle \ln(3^{3x+5}) = \ln(5)$

$\displaystyle (3x+5)\ln(3) = \ln(5)$

$\displaystyle 3x+5 = \frac{\ln(5)}{\ln(3)}$

can you finish now?
• Sep 25th 2009, 03:53 PM
katekate
yeah but with decimals again if that makes a difference.