Question

3^4x-7 =4^2x+3

Answer 1

Is that 3^(4x-7) = 4^(2x+3)? In other words, is 4x-7 the exponent on the left side?

Answer 2

yes

Answer 3

and 2x+3 is the exponent on the right

Answer 4

OK, hang on a sec ...

Answer 5

x = (-6 log2-7 log3) / (4 (log2-log3))

Answer 6

or about 7.31

Answer 7

can you explain how you got to that answer?

Answer 8

When you take the log of each side you get
(4x-7) log 3 = (2x-3) log 4

Answer 9

Solve for x the usual way (just treat the logs as any other numbers).

Answer 10

*above (2x-3) should be (2x+3), typo; didn't affect the answer

Answer 11

OK? No?

Answer 12

If you need it, the next step would be
4log3 x - 7log3 = 2log4 x + 3log4

Answer 13

okayy! thanksss!!!!

Answer 14

welcome

Answer 15

wait would you divide after the last step you did?

Answer 16

I would get the x terms on one side first:
(4log3-2log4) x = ...

Answer 17

3log4+7log3 would be the right-hand side :)

Answer 18

Then divide each side by (4log3-2log4).

Answer 19

thank you so much!!

Answer 20

The only other trick I used that you might not see is 3log4 = 3log(2^2) = 6log2.

Answer 21

thanks!! :D