Question

12. 8.2 (x+1) = 55
15. 72 (2x) = 35

Answer 1

Explanation:

8.2^(x+1) = 55

x + 1 = log(55)/log(8.2)

x = log(55)/log(8.2) - 1 = 0.904504604...

72^(2x) = 35

2x = log(35)/log(72)

x = log(35)/log(72) / 2 = log(35)/(2×log(72)) =

= 0.415668182...

Answer 2

12. 0.9045

15. 0.4157

Explanation:

These are solved by taking logarithms, then solving the resulting linear equation. The applicable rule of logs is ...

log(a^b) = b·log(a)

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12. (x+1)log(8.2) = log(55) . . . . . take the log of both sides

x +1 = log(55)/log(8.2) . . . . . . divide by log(8.2)

x = log(55)/log(8.2) -1 = 1.9045 -1 = 0.9045

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15. (2x)log(72) = log(35 . . . . . . . take the log of both sides

x = log(35)/(2·log(72)) . . . . . . . divide by the coefficient of x

x ≈ 0.4157