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Solve the equation. Round to the nearest hundredth. 4(1.15)^x = 12 a. x ≈ 3.00 b. x ≈ 12.00 c. x ≈ 7.86 d....

23. Solve the equation. Round to the nearest hundredth.
4(1.15)^x = 12
a. x ≈ 3.00
b. x ≈ 12.00
c. x ≈ 7.86
d. x ≈ 5.18

Answer

To solve the equation 4(1.15)x = 12, first divide both sides by 4:

(1.15)x = 3

Take the logarithm of both sides:

log((1.15)x) = log(3)

x * log(1.15) = log(3)

x = log(3) / log(1.15)

Calculate x:

x ≈ 7.86

Correct answer: c. x ≈ 7.86

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