Multiple Choice
Rewrite the log expression as a difference of multiple logs. Further simplify if possible.
11. Inverse, Exponential, & Logarithmic Functions
Properties of Logarithms
Multiple Choice
Rewrite the difference as a single logarithm. Further simplify if possible.
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Verified step by step guidance1
Recall the logarithmic property that states the difference of two logarithms with the same base can be rewritten as the logarithm of a quotient: \(\log_{10} A - \log_{10} B = \log_{10} \left( \frac{A}{B} \right)\).
Apply this property to the given expression: \(\log_{10} (8x^2) - \log_{10} (2x) = \log_{10} \left( \frac{8x^2}{2x} \right)\).
Simplify the fraction inside the logarithm by dividing the coefficients and the variables separately: \(\frac{8x^2}{2x} = \frac{8}{2} \times \frac{x^2}{x}\).
Calculate the simplified fraction: \(\frac{8}{2} = 4\) and \(\frac{x^2}{x} = x^{2-1} = x\), so the expression inside the logarithm becomes \$4x$.
Rewrite the expression as a single logarithm with the simplified argument: \(\log_{10} (4x)\).
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