Question

Solve the following equation for x:

Answer 1

3^4^x^-^5 = (1/27)^2^x^+^10

Answer 2

If that's confusing, let me use words:
4x-5 is all an exponent of 3. 2x+10 is all an exponent of (1/27)

Answer 3

you have to convert both bases to the same number

for example, (1/27) can be re-written as 3^(-3)

Answer 4

Okay, so once I do that, would I solve the equation as I normally would with say 2x-15=20? Except I do most of the work with the exponents?

Answer 5

so 3^(4x-5) stays the same since it's already in base 3

(1/27)^(2x+10) becomes (3)^(-3*(2x+1))

then you can just set the exponent parts equal to each other and solve for x

Answer 6

so 4x - 5 = -3(2x+10)

Answer 7

Okay, so I'd add 5 first. Then divide by 4 for all terms, making:
x=-3/4(2x/4+15)
Right?

Answer 8

I would recommend distributing first

Answer 9

4x - 5 = -3(2x+10)

becomes

4x - 5 = -6x - 30

then combine like terms

Answer 10

That makes more sense. So now I'd add 6x to both sides and add 5 to both sides making:
-2x = 35
Right? Or would it be -2x = -25 ? Negatives in equations sometimes mess my brain up for some reason.

Answer 11

if you add 6x to both sides you end up with 4x + 6x = 10x on the left hand side

Answer 12

so it ends up being 10x = -25

Answer 13

So both of my ideas were wrong. Okay. Thanks for the help, I really appreciate it.