Exponential Equation Worksheet With Answers Page 3
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1
2
3
4
5
6
72x
19) 32e
= 128 (divide each side by 32)
2x
e
= 4 (take ln of each side)
2x
ln e
= ln 4 (use power to product rule)
2x(ln e)= ln 4 (ln e = 1)
2x = ln 4 (divide by 2)
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Answer: x =
= .69
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x-1
x
21) 3
= 5
(take log of both sides)
x-1
x
Log(3
) = log(5
) (use power to product rule)
(x-1)log(3) = x(log 5)
x( log 3) – log(3) = x( log 5) (move the xlog(5) to left and –log(3) to right)
x(log 3) – x(log 5)= log(3) (factor out GCF of x)
x( log 3 – log 5 )= log(3) (divide)
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Answer: �� =
= −��. ����
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x-1
x
23) 6
= 9
(take log of both sides)
x-1
x
Log(6
) = log(9
)
(use power to product rule)
(x-1)log 6 = x(log 9 )
x(log 6) – log(6) = x(log 9) (move the x(log 9) to left and –log(6) to right)
x(log 6) – x(log 9) = log(6) (factor out GCF of x)
x( log(6) – log(9) ) = log(6) (divide)
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Answer: �� =
= −��. ����
������ ( �� ) −������ (��)
#25 - 51: Solve the logarithmic equations, round to 2 decimals when needed.
25) log
x = 2
3
2
3
= x
Answer: x = 9
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