3^(5x-6) =81 Solve for x?

Take logs to base 3
(5x - 6) log 3 = log 81
5x - 6 = 4
5x = 10
x = 2

3^(5x-6)=3^4
5x-6=4
5x=10
x=2
why? sub x=2 to ur original question
check: 3^(5*2-6)=3^4=81
therefore x=2!!!!!

Okay, this is technically where a logarithm comes into play. If you haven't done that before, that's fine, I'll try to make it simple.

Since the x is part of our exponent, you need to bring it down. You do this by finding log on both sides.

log(3)(5x-6) = log(81)

We only put the three in parentheses because that's how we bring down our exponent.

Now divide log(81) by log(3)

5x-6 = log(81)/log(3)

You don't have to know how to do it really if you have a calculator. I'm not going to show you the work. However, your answer for log(81)/log(3) = 4 (This means if you did 3^4 you'd get 81)

Now we have 5x-6 = 4

Move the 6 over to the right

5x = 10

Divide out 5.

x = 2

Now if you knew that 81 was 3^4 already, you probably could have done this in the shorter way. I'm just teaching the log thing because sometimes you won't know the exact exponent.

I hoped that helped.

lala's answer was very smart ... it only works that easily because 81 is a multiple of 3

If you couldn't do 3*3*3*3 = 81, lets say you had 95 for example.

You would do the change of base formula for log's:

so if 3^(5x-6)=95

you take log base 3 of both sides. the log base three on the left cancels out the base of 3 and you're left with

5x-6 = log base 3 of 95

5x = log base 3 of 95 + 6

to get log base 3 of 95, you do ln(95) / ln(3). it only matters that the base of these two logs is the same. use 10 or LN since it's on your calculator

so

x = LN(95)/LN(3) + 6 , all divided by 5

or in your case,

x = LN(81)/LN(3) + 6 , all divided by 5 = 2

a million) x -9 = 0 =>x = 9 or x + 8 = 0 => x = - 8 2) (x - 9)(x - 12) = 0 => x = 9 or x = 12 3) (2s + 3)(s - 8) = 0 => x = -3/2 or s = 8 4) (3n + 36)(n - 8) = 0 => n = -12 or n = 8 5) (c - 9)(c + 9) = 0 => c = 9 or - 9 6) x^2 + 35x + 306 = 0 (x + 17)(x + 18 ) = 0 => x = - 17 or x = - 18

5x - 6 = ln 81/ln3 //take natural log of both sides by dividing
natural log of 81 into natural log of 3.

5x - 6 = 4 //this is result
5x = 6 + 4 // add 6 to both sides
5x = 10 //this is the result
x = 2 //divide by 5 and you get x = 2

3^(5x - 6) = 81
3^(5x - 6) = 3^4
5x - 6 = 4
5x = 4 + 6
x = 10/5
x = 2

3^(5x-6) =81
3^(5x-6)=3^4
5x-6=4
add 6 on both sides
5x-6+6=4+6
5x=10
divide 5 from both sides
5x/5=10/5
x=2

3(5x-6)=81
15x-30=81
15x=111
x=7.4

(5x - 6) = 81

5x = 81 + 6
5x = 87
x = 87 / 5
x = 17.4