Question

5^x=3^(x+1)
How do I solve this type of problem?

Answer 1

Use logarithms.

ln(5^x) = ln(3^(x+1))
x ln(5) = (x+1) ln(3)

x (ln5-ln3) = ln3
x = ln3/(ln5-ln3)

Answer 2

Medal?

Answer 3

where did you get the ln from? wouldn't it be log?

Answer 4

ln is log to base e.

Answer 5

i know that, but why did you change log to ln?

Answer 6

It is written as "ln" too. Same thing.

Answer 7

LN

Answer 8

ok, i understand the first part of solving it, but then how do you get to the next one? (3rd line)

Answer 9

x ln(5) = (x+1) ln(3)
x ln(5) = x ln(3) + 1*ln(3)
x ln(5) - x ln(3) = ln(3)
x (ln(5)-ln(3)) = ln(3)

Answer 10

what property allows you to separate the x+1 on line 2?

Answer 11

distributive
a(b+c) = ab + ac

Answer 12

but on logs isn't it logxy=logx+logy? is that the same as distributive?

Answer 13

In this case, you just have a constant ln(3). Treat it as any constant. And, (x+1) is not "inside the log function". So, treat it as just regular terms.

Answer 14

ok, so if there were parentheses it wouldn't work?

Answer 15

If it was 3*ln(x+1), then, you can't write it as 3*ln(x) + 3*ln(1).

Answer 16

ok, so how do you solve it once you get to x (ln(5)-ln(3)) = ln(3)?

Answer 17

x = ln3/(ln5-ln3)

Answer 18

Now, use calculator to find the value.

Answer 19

ok thanks :)

Answer 20

2.15 seems to be the answer.