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Solve the exponential equation 7 raised to the power x equal to 30. What is the exact answer?
Ax = log 30 divided by log 7
Bx = log 7 divided by log 30
Cx = log 30 minus log 7
Dx = 30 divided by 7
Answer & Solution
Correct answer: A. x = log 30 divided by log 7
1. The two sides cannot be written as powers of a common base, so a logarithm is needed.
2. The exponential is already alone, so take the logarithm of both sides.
3. That gives log of 7 to the power x equal to log of 30.
4. The power rule brings the exponent down in front, giving x times log 7 equal to log 30.
5. Divide both sides by log 7 to isolate x.
6. So x equals log 30 divided by log 7.
7. Flipping the fraction would answer the different question of what power of 30 gives 7.
8. Subtracting the logarithms would answer a division inside a single logarithm instead.
9. Dividing 30 by 7 ignores the exponent entirely and gives a value under 5, which is far too large.
_Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.5 Solve Exponential and Logarithmic Equations_