Answer:
x = 10
Explanation:
Combining the logarithms, you have ...
ln(20·5) = ln(x²)
100 = x² . . . . . take the antilogs
10 = x . . . . . . . take the positive square root
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Alternate solution
ln(2·2·5) +ln(5) = 2·ln(x) . . . . . . . factor 20
2ln(2) +ln(5) +ln(5) = 2·ln(x) . . . . rearrange ln(20)
ln(2) +ln(5) = ln(x) . . . . . . . . . . . . divide by 2
ln(10) = ln(x) . . . . . . . . . . . . . . . . combine logs on the left
10 = x
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These solutions make use of the rules of logarithms ...
ln(ab) = ln(a) +ln(b)
ln(a²) = 2·ln(a) . . . . . same as the first rule for a=b