Without a calculator, solve for x: 2(32)^x= 8(4)^3x you have to use logarithms somehow
\[2(32)^x = 8(4)^{3x}\]
apply ln to both side
Check out these rules real quick. http://www.rapidtables.com/math/algebra/Ln.htm
and use log properties to simplify
do i use the power law first ?
First have to figure out what Log and base to use.
can you pick ? :S
no. :D
then how do we know which is which
I'll give an example though: \[\huge \log_{10}(10^x) =x\] \[\huge \log_2(2^x)=x\]
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.
yeah but the question has on log stated
how is base determined tho? Is it just guessing?
Kind of... You get to choose the base. In your case, i would choose base two, because it will help simplify things.
Ohhhh, so the base is just determined by choice there's no specific rule to follow
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.
Gotta walk down to the store real quick. bbiab. :D
Honestly, there is no reason to use logarithms here...unless you are required for some other reason...
i know haha, but we're required to do so
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