Solve. (√7)^6x = 49^x–6

Possible Answers:

A) x = -12

B) x = -6/5

C) x = -21/2

D) x = -6

Please this question is driving me crazy, I would like to know how to solve it, thanks!

(√7)^6x = 49^x–6
7^(6x/2) = 7^(2x-12)
3x = 2x-12
x = -12
Answer A) x = -12

I assume you mean that the exponent of 49 is x - 6

(√7)^(6x) = 49^(x–6)

√7 = 7^(1/2)... so:

[7^(1/2)]^(6x) = (7^2)^(x-6)

7^(3x) = 7^[2(x - 6)]

Same base, so the exponent is the same:

3x = 2(x - 6)

3x = 2x - 12

x = -12

Remember that (a^m)^n = a^(m*n)

I hope this helps...

Do you mean:
(sqrt(7))^(6x) = 49^(x - 6)
log((sqrt(7))^(6x)) = log(49^(x - 6))
6x*log(sqrt(7)) = (x - 6)*log(49)
6x*log(sqrt(7)) = x*log(49) - 6*log(49)
x*log(49) - 6x*log(sqrt(7)) = 6*log(49)
x(log(49) - 6*log(sqrt(7)) = 6*log(49)
x = (6*log(49)) / (log(49) - 6*log(sqrt(7))
x = -12

NOTE: All logs above must be in the same base, but it doesn't matter what base you use (e.g. 10, e, etc).

The answer is A)

Proof

(√7)^6x = 49^(x–6)?

ln((√7)^6x) = ln(49^(x–6))?

6xln(√7) = (x-6)ln49

where ln49 = ln(√7^4) = 4ln(√7)

6xln(√7)=4(x-6)ln(√7)

6x = 4(x-6)

6x-4x=-24

2x = -24

x = -12

(√7)^6x = 49^(x–6)
==>[(7)^(1/2)]^6x = (7^2)^(x - 6)
==>7^3x=7^(2x-12)
==> 3x = 2x-12
==> x=-12

A) -12

Take logs of both sides

6xlogr7 = xlog49-6log49
6xlogr6-xlog49 = -6log49
x(6logr7-log49) = -6log49
x = -6log49/(6logr7-log49)

X=-12

(7^1/2)^6x=(7^2)^x-6
7^3x=7^2x-12
3x=2x-12
x=12