Question

Without a calculator, solve for x: 2(32)^x= 8(4)^3x

you have to use logarithms somehow

Answer 1

\[2(32)^x = 8(4)^{3x}\]

Answer 2

apply ln to both side

Answer 3

Check out these rules real quick. http://www.rapidtables.com/math/algebra/Ln.htm

Answer 4

and use log properties to simplify

Answer 5

do i use the power law first ?

Answer 6

First have to figure out what Log and base to use.

Answer 7

can you pick ? :S

Answer 8

no. :D

Answer 9

then how do we know which is which

Answer 10

I'll give an example though:
\[\huge \log_{10}(10^x) =x\]
\[\huge \log_2(2^x)=x\]

Answer 11

It's all about picking the right base so that you can either 1)calculate the log after pulling out an exponent. or 2)so that things simplify.

Answer 12

yeah but the question has on log stated

Answer 13

how is base determined tho? Is it just guessing?

Answer 14

Kind of... You get to choose the base. In your case, i would choose base two, because it will help simplify things.

Answer 15

Ohhhh, so the base is just determined by choice there's no specific rule to follow

Answer 16

Nope, not when choosing the base. The "rule" to follow is to just try and pick a base that helps simplify both sides of the equation. So in your case base 2 helps because you can use other log rules(multiply rule) to then begin to solve for x and such.

Answer 17

Gotta walk down to the store real quick. bbiab. :D

Answer 18

Honestly, there is no reason to use logarithms here...unless you are required for some other reason...

Answer 19

i know haha, but we're required to do so