1. ## Logarithm Problems

How would one solve for x in the following, using the laws of logarithms?

1) 5^x+3^2x=92

2) 4*5^x-3*0.4^2x=11

In 1), this is what I've done so far:

5^x+3^2x=92
log(5^x+3^2x)=log 92
log(5+3^2)^x=log 92
x log 14=log 92

but I don't think that it's correct, and things aren't any clearer for question 2).

2. Hello DemonX01
Originally Posted by DemonX01
How would one solve for x in the following, using the laws of logarithms?

1) 5^x+3^2x=92

2) 4*5^x-3*0.4^2x=11

In 1), this is what I've done so far:

5^x+3^2x=92
log(5^x+3^2x)=log 92
log(5+3^2)^x=log 92
x log 14=log 92

but I don't think that it's correct, and things aren't any clearer for question 2).
For number (1), you're right: your working is not correct.

However, I don't know what method you are supposed to use to solve these equations. The only way I can see is to use some sort of approximate numerical method. Doing this, I can tell you that the answers are: (1) 1.9311, and (2) 0.6758, correct to 4 d.p.

But I cheated a bit and used a spreadsheet.

3. Remember that $3^{2x}=(3^2)^x$
$5^x+9^x=92$