Question

3^2x-3=5^x+2 solve this equation in terms of the natural logarithm. Give an approximation to the nearest hundreth of a unit.

Answer 1

\[
3^{2x}-3=5^x+2
\]is this how it is?

Answer 2

no the exponent is 2x-3 and x+2

Answer 3

add ln on both sides

Answer 4

so,
\[\Large{
3^{2x-3}=5^{x+2}\\
3^{2x}3^{-3}=5^x5^2\qquad\text{split the exponent}\\
\text{now, bring the 'x' terms together}\\
\frac{3^{2x}}{5^x}={5^2\over 3^{-3}}\\
\left(3^2\over 5\right)^x=5^23^3\\
\left(9\over 5\right)^x=25\times 27\
}\]now, take the logarithm

Answer 5

when you take the logrithm now, the exponent "x" will come down by property

Answer 6

supposed to be the natural logarithm

Answer 7

you are free to use any logarithm base.

Answer 8

oh ok well for this problem it asks to use natural

Answer 9

then use it.
there is another way for this too..
\[\Large{
3^{2x-3}=5^{x+2}\\
\ln(3^{2x-3})=\ln(5^{x+2})\\
(2x-3)\ln(3)=(x+2)\ln(5)
}\]then simplify this further

Answer 10

I used the property
\[\log(a^m)=m\times \log(a)\]

Answer 11

kapeesh?

Answer 12

ya I dont know how to simplify it further though

Answer 13

Im terrible with this stuff

Answer 14

use a calculator to find the logs.
on your calculator there should be a button that says "ln"=natural log and "log"=log base 10

Answer 15

so take the ln of 3 and the ln of 5

Answer 16

yes

Answer 17

then what?

Answer 18

then show me what you got

Answer 19

(2x-3)(1.10)=(x+2)(1.61)

Answer 20

now, we expand the paranthesis..

Answer 21

2.2x-3.3=1.61+3.22

Answer 22

1.61x

Answer 23

great.