Alg 2 help?

Question

simplify the expression: 3e^x / e^3x * e^-2x / 12

Solve: 1/8 = 4^4x-5

Solve for x: 7.43^x = 38

Answer 1

simplify the expression: 3e^x / e^3x * e^-2x / 12

e^-4x / 4

Solve: 1/8 = 4^4x-5

I'm not sure what all should be in the exponent, so I will guess it is 1/8 = 4^(4x-5). Taking the log base 2 of both sides gives:
-3 = 2(4x -5), then solving for x gives us x=7/8

Solve for x: 7.43^x = 38

Taking the log (any log you want, base 10 is fine) of both sides gives you x = log38/log7.43

Answer 2

1/8 = 4^4x-5
2-³ = 2²(4x-5)
Operating exponents:
-3 = 2(4x-5)
-3 = 8x - 10
-3 + 10 = 8x
8x = 7
x = 7/8
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