Question

6^(x - 3) = 52

Answer 1

\[6^{x - 3} = 52\]

Answer 2

i know how to do it when it's just 6^x = 52 but now that they threw in the x - 3 i don't know what to do.

Answer 3

\[6^{x-3}=52\iff x-3=\frac{\ln(52)}{\ln(6)}\] by the change of base formula

Answer 4

same idea
take the log of both sides

use the rule
\[ \log(a^b) = b \log(a) \]

Answer 5

the \(-3\) is a red herring
just add 3 at the end

Answer 6

do i plug 52 in for a?

Answer 7

so the problem (after taking the log of both sides) is
(x+3) log(6) = log(52)

log(6) is just a number. divide both sides by log(6)
(x+3)= log(52)/log(6)
or
x+3 = log(52)/log(6)
add -3 to both sides

x= log(52)/log(6) - 3

it is now calculator time if you want to get a number...

Answer 8

i got a negative number...

Answer 9

that is because I made a typo

it is x-3 = log(52)/log(6)
so
x = log(52)/log(6)+3

Answer 10

i was wondering why you changed signs but i didn't know if that was part of some weird rule.

Answer 11

once you get an answer, you can check it in the original equation to make sure it works.

Answer 12

now if i have
\[10^{x + 4} = 1000\]

can i do
\[10^{x + 4} = 10^{2}\]

and then what

Answer 13

you mean 10^3 (10^2 is 10*10= 100)

if the bases are equal, you can set the exponents equal and solve
x+4 = 3

or, if you use logs:

log( 10^(x+4) ) = log(10^3) (log is base 10) so this gives you
(x+4) log(10) = 3 log(10)

log base 10 of 10 is 1, and you get
x+4 = 3
which matches the first (and faster) way

Answer 14

gotcha. okay that is easy.