Solve each equation. Round decimal answers to the nearest thousandth.

Question

5(0.10)^x = 4(0.12)^x

Answer 1

5(0.10)^x = 4(0.12)^x.

Take log of both sides:
log5 + xlog(0.10) = log4 + xlog(0.12)0.6990 - x = 0.6021 - 0.9208x,
-x + 0.9208x = 0.6021 - 0.6990,
-0.0792x = -0.0969,

X = -0.0969 / -0.0792 = 1.22.

Answer 2

CORRECTION:

Take log of both sides:
log5 + Xlog(0.10) = log4 + Xlog(0.12),
0.6990 - X = 0.6021 - 0.9208X,
-x + 0.9208X = 0.6021- 0.6990,
-0.0792X = -0.0969,

X = -0.0969 / -0.0792 = 1.22.