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

you have to use logarithms somehow

Question

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

anonymous · Answer

$$2(32)^x = 8(4)^{3x}$$

anonymous · Answer

apply ln to both side

anonymous · Answer

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

anonymous · Answer

and use log properties to simplify

anonymous · Answer

do i use the power law first ?

anonymous · Answer

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

anonymous · Answer

can you pick ? :S

anonymous · Answer

no. :D

anonymous · Answer

then how do we know which is which

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

yeah but the question has on log stated

anonymous · Answer

how is base determined tho? Is it just guessing?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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