Solve for x 5(2)^3x-4=13

Answer 1

Question: Solve for x: 5(2)^3x - 4 = 13.

Answer: Add 4 to both sides.

5(2)^3x = 17

Divide both sides by 5.

2^3x = (17/5)

Take log₂ of both sides.

log₂2^3x = log₂(17/5)

The left-hand side simplifies to 3x.

3x = log₂(17/5)

Divide both sides by 3.

x = (1/3)log₂(17/5) <--- Exact answer.

To find an approximation, apply change of base to the log expression using a calculator and divide the result by 3.

x = (1/3)(log (17/5) / log 2)

Answer 2

If this is the problem:

5(2)^(3 x) - 4 = 13 add 4 to both sides then divide by 5

2^(3x) = 17/5 Take the log of both sides bring the exponent down:

3x(log 2) = log (17/5)

3x( log 2) = log (17) - log (5) divide by 3• log(2)

x = [ log(17) - log(5)]/[ 3• log(2)]

punch it in on your calculator

the way the question is written the x is not in the exponent:

5(2)^3 x - 4 = 13 , add 4 and cube 2

5 • 8 x = 17, 40 x = 17

x = 27/40 not sure which you meant?

5

Answer 3

Your formatting is a little confusing, so let me know if I'm interpreting this incorrectly.

5 * 2^{(3x - 4)} = 13

divide both sides by 5 to isolate the exponential part of our equation

2^{(3x - 4)} = 13/5

log base 2 both sides to bring our exponent down and work with it

3x - 4 = log2(13/5)

add 4 on both sides to isolate our monomial (3x)

3x = log2(13/5) + 4

divide both sides by 3

x = (log2(13/5) + 4)/3 = 1.793

Check out Cristian's answer if the -4 is not part of the exponent.