Question

Which of the following is the solution to the equation 36^3c = sqrt(6)^(6c + 8)?

a. c = -3/2
b. c = -4/3
c. c = 4/3
d. c = 3/2

Answer 1

\[c=\frac{4}{3} \]

Answer 2

how?

Answer 3

\[36^{3c}= \left(\sqrt{6}\right)^{6c+8}\]\[\log \left(36^{3 c}\right)=\log \left(6^{\frac{1}{2} (6 c+8)}\right) \]\[3 c (2 \log (2)+2 \log (3))=\frac{1}{2} (6 c+8) (\log (2)+\log (3)) \]\[3 c \log (3)+3 c \log (2)-4 \log (3)-4 \log (2)=0 \]\[3 c =\frac{-4 \text{Log}[2]-4 \text{Log}[3]}{(\text{Log}[2]+\text{Log}[3])}\]\[3 c=-4\]

Answer 4

oh ok thanks.. not really understandin though

Answer 5

Take the log of each side. Move the RHS to the LHS, expand and simplify. Then solve for c.

Answer 6

so its -4/3?

Answer 7

Yes.

Answer 8

b/c in the beginn u said 4/3 is that wrong...

Answer 9

The answer is 4/3. First the problem was solved with Mathematica. Then you wanted the solution steps which is understandable. So I took a shot at solving it by hand and got it wrong. I probably should not participate on this forum any longer.

I believe the process is correct.

Answer 10

ok, so what u are saying is taht the first answer was right, 4/3 and the second was wrong.?

Answer 11

36^(3c) = sqrt(6)^(6c + 8)

(6^2)^(3c) = (6^(1/2))^(6c+8)

(6)^(2(3c)) = (6)^((1/2)(6c+8))


Since the bases are equal ( to 6), the exponents must be equal


2*3c = (1/2)(6c+8)

6c = (1/2)(6c+8)

6c = (1/2)(6c)+(1/2)(8)

6c = 3c+4

6c-3c = 4

3c = 4

c = 4/3


So the solution is c = 4/3

Answer 12

If you replace c with +4/3, then both sides of the problem equation should calculate out to 1679616 for both sides of the equation.

Answer 13

ok i see that thanks!