Multiple Choice
Rewrite the log expression as a sum of multiple logs. Further simplify if possible.
11. Inverse, Exponential, & Logarithmic Functions
Properties of Logarithms
Multiple Choice
Rewrite the sum as a single logarithm. Further simplify if possible.
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Verified step by step guidance1
Recall the logarithm property that states the sum of two logarithms with the same base can be rewritten as the logarithm of the product of their arguments: \(\log_{b} A + \log_{b} B = \log_{b} (A \times B)\).
Apply this property to the given expression \(\log_{10} x + \log_{10} (x+2)\), rewriting it as \(\log_{10} \bigl(x \times (x+2)\bigr)\).
Multiply the expressions inside the logarithm: \(x \times (x+2) = x^2 + 2x\).
Rewrite the expression as a single logarithm: \(\log_{10} (x^2 + 2x)\).
Check if the expression inside the logarithm can be factored or simplified further. In this case, \(x^2 + 2x\) can be factored as \(x(x+2)\), but since the logarithm of a product is the sum of logarithms, the simplified single logarithm form is already achieved.
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