Exponential question-Need Help!?

Question

I'm having trouble answering this question: 1/4=8^9x+5. The study guide gives the answer as -17/27, but I can't get the answer. Thanks for the help.

Answer 1

Let's rewrite both bases as powers of 2:

2^ -2 = (2^3)^(9x+5)
2^ -2 = 2^(27x + 15)

Once you have the same base on either side, you can equate the exponents:

-2 = 27x + 15
-17 = 27x
x = -17/27

Answer 2

1/4 = 8^(9x + 5)

4 is equal to 2^2, so

1/(2^2) = 8^(9x + 5)

8 is equal to 2^3, so

1/(2^2) = (2^3)^(9x + 5)

Whenever we have a power to a power, we multiply the exponents, so we multiply the 3 with the (9x + 5).

1/(2^2) = 2^(27x + 15)

And lastly, one over x is the same as x^(-1), so we have

[ 2^(2) ]^(-1) = 2^(27x + 15)

And, by the property discussed earlier, whenever we have a power to a power, we can multiply.

2^(-2) = 2^(27x + 15)

Same base, different exponent, equality. Equate the exponents.

-2 = 27x + 15

Solve for x.

-17 = 27x, so

x = -17/27

Answer 3

1/4 = 8^(9x+5)
2^(-2) = 2^3^(9x+5)
Now you can set the exponents equal:
-2 = 3(9x=5)
-2 = 27x + 15
-17 = 27x
-17/27 = x

Answer 4

Do you mean 1/4=8(9x+5)?
If this is the case, you can rewrite this as 2^(-2)=2^[3(9x+5)]
Therefore, -2=3(9x+5)
-2/3=9x+5
-2/3-5=9x
-17/3=9x
-17/27=x

Answer 5

We'll use log (base 2), so

log(1/4) = log(8^(9x + 5))
log (1) - log(4) = (9x + 5)log(8)
0 - 2 = (9x + 5)3
-2 = 27x + 15
-2 - 15 = 27x
x = -17/27

HTH

Charles

Answer 6

(1/4) = 8^(9x + 5)
2^(-2) = (2^3)^(9x + 5)
2^(-2) = 2^(3(9x + 5))
2^(-2) = 2^(27x + 15)

27x + 15 = -2
27x = -17
x = (-17/27)