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Rewriting expressions of the form $\\log(a)\\pm \\log(b)$ as a single logarithm.

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Rewrite the following expression as a single logarithm:

\n

\\[\\simplify{log({a})+{n}log({b})}.\\]

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{advice}

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To rewrite $\\\\log(\\\\var{a})+\\\\log(\\\\var{b})$ as a single logarithm, we want to use the rule \\\\[ \\\\log(a)+\\\\log(b) = \\\\log(ab).\\\\]

\\n

Hence,

\\n

\\\\[ \\\\log(\\\\var{a})+\\\\log(\\\\var{b}) = \\\\log(\\\\var{a*b}).\\\\]

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To rewrite $\\\\log(\\\\var{a})-\\\\log(\\\\var{b})$ as a single logarithm, we want to use the rule \\\\[ \\\\log(a)-\\\\log(b) = \\\\log\\\\left(\\\\frac{a}{b}\\\\right).\\\\]

\\n

Hence,

\\n

\\\\[ \\\\log(\\\\var{a})-\\\\log(\\\\var{b}) = \\\\log\\\\left(\\\\simplify[fractionNumbers]{{a/b}}\\\\right).\\\\]

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[[0]]

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