1) 4^x - 6 = 4
4^x = 10
log(4^x) = log(10)
x * log(4) = 1
x = 1 / log(4)
x ≈ 1.6609
2) 3e^(2x) = 12
e^(2x) = 4
ln(e^(2x)) = ln(4)
2x = ln(4)
x = ln(4) / 2
x ≈ 0.6931
3) 10^(x+2) - 12 = 22
10^(x+2) = 34
log(10^(x+2)) = log(34)
x + 2 = log(34)
x = log(34) - 2
x ≈ -0.4685
4) 3e^x + 7 = 9
3e^x = 2
e^x = 2/3
ln(e^x) = ln(2/3)
x = ln(2/3)
x ≈ -0.4055
5) 3(2^(x+6)) - 4 = 17
3(2^(x+6)) = 21
2^(x+6) = 7
log(2^(x+6)) = log(7)
(x + 6) * log(2) = log(7)
x + 6 = log(7) / log(2)
x = log(7) / log(2) - 6
x ≈ -3.1850
6) 4e^(3x) - 8 = -6
4e^(3x) = 2
e^(3x) = 0.5
ln(e^(3x)) = ln(0.5)
3x = ln(0.5)
x = ln(0.5) / 3
x ≈ -0.2310
7) 2 * 10^(2x-3) + 3 = 19
2 * 10^(2x-3) = 16
10^(2x-3) = 8
log(10^(2x-3)) = log(8)
2x - 3 = log(8)
2x = log(8) + 3
x = (log(8) + 3) / 2
x ≈ 1.9515
8) 7^(2x-3) - 4 = 14
7^(2x-3) = 18
log(7^(2x-3)) = log(18)
(2x - 3) * log(7) = log(18)
2x - 3 = log(18) / log(7)
2x = log(18) / log(7) + 3
x = (log(18) / log(7) + 3) / 2
x ≈ 2.2856
Parent Tip: Review the logic above to help your child master the concept of solving exponential equations worksheet with answers.
