Answer:
x = 2 log 2 / (log 5 − log 2)
x = log 4 / log(2.5)
Step-by-step explanation:
2ˣ⁺² = 5ˣ
Take log of both sides.
log(2ˣ⁺²) = log(5ˣ)
Use exponent property.
(x + 2) log 2 = x log 5
Distribute.
x log 2 + 2 log 2 = x log 5
Subtract x log 2 from both sides.
2 log 2 = x log 5 − x log 2
Factor out x.
2 log 2 = x (log 5 − log 2)
Solve for x.
x = 2 log 2 / (log 5 − log 2)
If you want, you can simplify further:
x = log 4 / log(2.5)
