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Mathematics 77 Online
OpenStudy (anonymous):

Without a calculator, solve for x: 2(32)^x= 8(4)^3x you have to use logarithms somehow

OpenStudy (anonymous):

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

OpenStudy (anonymous):

apply ln to both side

OpenStudy (anonymous):

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

OpenStudy (anonymous):

and use log properties to simplify

OpenStudy (anonymous):

do i use the power law first ?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

can you pick ? :S

OpenStudy (anonymous):

no. :D

OpenStudy (anonymous):

then how do we know which is which

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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.

OpenStudy (anonymous):

yeah but the question has on log stated

OpenStudy (anonymous):

how is base determined tho? Is it just guessing?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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.

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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