How to solve exponential equation for 4^(3m-1) • 32^(2m-3) = 4

9.5/8 = 1.1875

Step-by-step explanation:

4^(3m-1) • 32^(2m-3) = 4

4^(3m-1) • (4^2.5)^(2m-3) = 4

Law of exponents

3m-1 + 2.5(2m-3) = 1

3m - 1 + 5m - 7.5 = 1

8m = 1 + 1 + 7.5

8m = 9.5

m = 9.5/8

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.