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To solve the equation 5^x = 15, you can take the logarithm of both sides. By taking the natural logarithm of both sides, you get x * ln(5) = ln(15). Then, you can solve for x by dividing both sides by ln(5), giving you x = ln(15) / ln(5), which is approximately 1.682.
Using logarithms. In economics, we most commonly use the the base e, which is known as ln. For example
5^x = 15, apply ln[.] to both sides
ln[5^x] = ln[15]
and since logarithms have the property of turning exponents into coefficients
xln5 = ln15
x = ln15/ln5
x = 1.6826
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