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Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Simplify the expressions to fill in the gaps.

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a)

We need to use the rule

\\[\\log_a(x)+\\log_a(y)=\\log_a(xy)\\text{.}\\]

Substituting in our values for $x$ and $y$ gives

\\[\\begin{align}
\\log_a(\\var{x1[1]})+\\log_a(\\var{x1[0]})&=\\log_a(\\var{x1[1]}\\times \\var{x1[0]})\\\\
&=\\log_a(\\var{x1[1]*x1[0]})\\text{.}
\\end{align}\\]

b)

We need to use the rule

\\[\\log_a(x)-\\log_a(y)=\\log_a\\left(\\frac{x}{y}\\right)\\text{.}\\]

Substituting in our values for $x$ and $y$ gives

\\[\\begin{align}
\\log_a(\\var{x1[4]*y1})-\\log_a(\\var{x1[4]})&=\\log_a(\\var{x1[4]*y1}\\div \\var{x1[4]})\\\\
&=\\log_a(\\var{y1})\\text{.}
\\end{align}\\]

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$\\log_a(\\var{x1[1]})+ \\log_a(\\var{x1[0]})=\\log_a($ [[0]]$)$

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When adding and subtracting logarithms we can simplify the expressions using some logarithm laws. These laws are

\\[\\begin{align}
\\log_a(x)+\\log_a(y)&=\\log_a(xy)\\text{,}\\\\
\\log_a(x)-\\log_a(y)&=\\log_a\\left(\\frac{x}{y}\\right)\\text{.}
\\end{align}\\]

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$\\log_a(\\var{(x1[4])*y1})-\\log_a(\\var{x1[4]})=\\log_a($ [[0]]$)$

When adding and subtracting logarithms we can simplify the expressions using some logarithm laws. These laws are

\\[\\begin{align}
\\log_a(x)+\\log_a(y)&=\\log_a(xy)\\text{,}\\\\
\\log_a(x)-\\log_a(y)&=\\log_a\\left(\\frac{x}{y}\\right)\\text{.}
\\end{align}\\]

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$ \\log_a (\\var{x1[5]}^\\var{x1[6]}) $ = [[0]]$\\log_a$ ([[1]])

When adding and subtracting logarithms we can simplify the expressions using some logarithm laws. These laws are

\\[\\begin{align}
p \\log_a(x) &=\\log_a(x^p)\\text{.}\\\\
\\end{align}\\]

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