What is 2log_{10}(21)-log_{10}(x) ?

The solution to 2log_{10}(21)-log_{10}(x) is log_{10}((441)/x)

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simplify 2log_{10}(21)-log_{10}(x)

simplify

2 lo g_{10} (21) - lo g_{10} (x)

lo g_{10} (\frac{441}{x})

Solution steps

2 lo g_{10} (21) - lo g_{10} (x)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

2 lo g_{10} (21) = lo g_{10} (2 1^{2})

= lo g_{10} (2 1^{2}) - lo g_{10} (x)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (2 1^{2}) - lo g_{10} (x) = lo g_{10} (\frac{2 1 ^{2}}{x})

= lo g_{10} (\frac{2 1 ^{2}}{x})

Simplify

\frac{2 1 ^{2}}{x} : \frac{441}{x}

= lo g_{10} (\frac{441}{x})

ln (\frac{e ^{4}}{15})

\frac{- 6 ln ( 8 )}{ln ( 8 ) - ln ( 5 )}

ln (2) - ln (- 2)

ln (\frac{131}{2})

lo g_{10} (\frac{x}{y ^{2} z})

What is 2log_{10}(21)-log_{10}(x) ?
The solution to 2log_{10}(21)-log_{10}(x) is log_{10}((441)/x)