Question

Log question, let me write it out so it makes more sense!

Answer 1

\[f(x)=\log _{4}(x+2) AND g(x)=\log_{4}(2x-5), please find f(x)=g(x)\]

Answer 2

use the fact that if log A =logB then A =B
can you find an equation in 'x' using that ?

Answer 3

If log a = log b then a = b

Answer 4

f(x)=g(x)
implies x+2=2x-5
x=7

Answer 5

for any base, (base of 4 doesn't matter here)

Answer 6

Well, the answer is {7}, (log4(9))

Answer 7

I honestly have no idea how to solve that out, it's review and I can't find it in my notes.

Answer 8

for any log expressions with same base to be equal e.g log a = log b be it any base a = b
for you just have to simply work out a linear equation

Answer 9

can you clearly post your question ? a screenshot will be wonderful....

Answer 10

Solve the problem.
1 2 ) f(x) = log4(x + 2) and g(x) = log4( 2 x - 5) .
Solve f(x) = g(x).
1 2 )
A) {7} , (7, log4(7) ) B) {7} , (7, log4(9) ) C) {7} , (7, log4(2) ) D) No solution.
A n s w e r : B

Answer 11

It's the best I can do, sorry. And when you solve it as a linear equation, would you change it to exponencial form, or can you not do that?

Answer 12

you can change but that wouldn`t do any good......
a = e ^ (ln a) (basic property of log)

Answer 13

ok, did you get how x=7 ?
now just put x=7 in any one of f(x) or g(x)

Answer 14

I didn't get x=7, our teacher gave us the answers and I don't know how she got any of them. I'd really like to see someone solve the equation so I can see what you guys are talking about. ;P I tried doing it and got -7/2

Answer 15

if log A =logB then A =B
\(f(x)=g(x) \implies \log_4 (x+2)=\log_4(2x-5) \\ \implies x+2 = 2x-5\)
can you solve this linear equation ????

Answer 16

Yeah, it makes x=7. So to get the log4(9), you just put it into one of the equations?

Answer 17

correct, put in any one of f(x) or g(x)

Answer 18

and you'll get log4(9) part of your answer.

Answer 19

Thank you! (:

Answer 20

welcome ^_^