# Calculate: log_{10}(9)-2log_{10}(7)

## Expression: $\log_{ 10 }({ 9 })-2\log_{ 10 }({ 7 })$

Use $x \times \log_{ a }({ b })=\log_{ a }({ {b}^{x} })$ to transform the expression

$\log_{ 10 }({ 9 })+\log_{ 10 }({ {7}^{-2} })$

Use $\log_{ a }({ x })+\log_{ a }({ y })=\log_{ a }({ x \times y })$ to simplify the expression

$\log_{ 10 }({ 9 \times {7}^{-2} })$

Express with a positive exponent using ${a}^{-n}=\frac{ 1 }{ {a}^{n} }$

$\log_{ 10 }({ 9 \times \frac{ 1 }{ {7}^{2} } })$

Evaluate the power

$\log_{ 10 }({ 9 \times \frac{ 1 }{ 49 } })$

Calculate the product

$\log_{ 10 }({ \frac{ 9 }{ 49 } })$

Write the number in exponential form with the base of $\frac{ 3 }{ 7 }$

$\log_{ 10 }({ {\left( \frac{ 3 }{ 7 } \right)}^{2} })$

Use $\log_{ a }({ {b}^{c} })=c \times \log_{ a }({ b })$ to transform the expression

\begin{align*}&2\log_{ 10 }({ \frac{ 3 }{ 7 } }) \\&\approx-0.735954\end{align*}

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