Question

Find the solution to the equation 64^(4 – x) = 4^2x. Using complete sentences, explain the procedure used to solve this equation.

Answer 1

@SolomonZelman

Answer 2

Take the log of both sides, like this:

Answer 3

\[\log64^{(4-x)}=\log4^{2x}\]

Answer 4

Then bring down the exponents as the rules tell us:\[(4-x)\log64=(2x)\log4\]

Answer 5

oh ok

Answer 6

Then...\[\frac{ 4-x }{ 2x }=\frac{ \log4 }{ \log64 }\]

Answer 7

\[\frac{ 4-x }{ 2x }=.333\]\[4-x=2x(.333)\]\[4-x=.666x\]\[4=.666x+x\]\[4=1.666x\]\[2.4=x\]

Answer 8

Can you translate that into complete sentences using what I showed you?

Answer 9

yep, that makes sense. Thank you for the help :)