Question

What is the solution to the equation 36^3c = square root of 6^(8c – 6) ?

Answer 1

Did you square both sides yet?

Answer 2

square root of 36 is 6 and the square root of 6 is 2.4494897?

Answer 3

It doesn't exactly work like that

You can't take the square root of the 6 while it has an exponent attached to it

Answer 4

You have to square both sides to get rid of the square root.

Answer 5

can you walk me through this please?

Answer 6

I'm trying, but LaTeX is not working too well right now

Answer 7

\[36^{3c} = \sqrt{6^{(8c – 6)}}\]

Answer 8

That's what you probably started off with

Answer 9

Now you have to square both sides like this:
\[{(36^{3c})}^2 = ({\sqrt{6^{(8c – 6)}}})^2\]

Answer 10

yes

Answer 11

The square and the square root cancels to get this:
\[{(36^{3c})}^2 =6^{(8c – 6)}\]

Answer 12

Meanwhile on the left side of the equation, you multiply exponents 3c and 2 to get:

\[36^{(6c)} =6^{(8c – 6)}\]

Answer 13

Now, 36 can be expressed as \(6^2\), therefore we re-write the equation producing:

\[\large6^{2^{(6c)}} =6^{(8c – 6)}\]

Answer 14

But since both 2 and 6c are exponents we can express it as a multiplication producing:

\[6^{2{(6c)}} =6^{(8c – 6)}\]

Answer 15

Now since the bases on both sides of the equation are the same we can simply set the exponents on both sides equal to one another producing:

2(6c) = 8c - 6

Can you solve for c from here?

Answer 16

no Im still confused

Answer 17

Maybe reviewing rules of exponents will help

Answer 18

okay I tried working itout and I got 4/3?

Answer 19

Weird. I got something else.

Answer 20

can you work it out please?

Answer 21

2(6c) = 8c - 6
12c = 8c - 6
12c - 8c = -6
c(12-8) = -6
c(4) = -6
c = -6/4
c = -3(2)/2(2)
c = -3/2

Answer 22

okay, I see what I did wrong. Thank you