Question

7•4^4x-5=72

How can I solve this using the rules of logarithms?

Answer 1

\[\large \rm 7 \cdot 4^{4x-5}=72 ~~~OR~~~~7\cdot 4^{4x}-5 =72 \] which one ?
i think 2nd one

Answer 2

the first one @Nnesha

Answer 3

alright. in order to drop the power
first we need to get rid of any number/ variable front of the base
so what would you do to cancel out 7 from left side ?

Answer 4

log base of 7? @Nnesha

Answer 5

to both sides?

Answer 6

hmm we should cancel out 7 from left side fist than deal with log
it's 7 times 4^{4x-5} to cancel out 7 divide both sides by 7

Answer 7

so im left with 4^4x-5=72/7 @Nnesha

Answer 8

right now you can take log both sides.

Answer 9

so that would be log 4^4x-5= log 72/7 . Then i can bring the 4x-5 to the front like this:
4x-5 log 4=log 72/7? @Nnesha

Answer 10

looks good

Answer 11

i would divide 72/7 to get decimal

Answer 12

then divide log 4

Answer 13

Thank you! i got it from here. Thank you so much for guiding me! @Nnesha

Answer 14

alright good :)

Answer 15

my pleasure :)