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

The solution to 2log_{2}(10)-log_{2}(x) is 2+log_{2}((25)/x)

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

simplify

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

2 + lo g_{2} (\frac{25}{x})

Solution steps

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

2 lo g_{2} (10) = 2 + 2 lo g_{2} (5)

= 2 + 2 lo g_{2} (5) - lo g_{2} (x)

Apply log rule:

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

2 lo g_{2} (5) = lo g_{2} (5^{2})

= 2 + lo g_{2} (5^{2}) - lo g_{2} (x)

Simplify

lo g_{2} (5^{2}) - lo g_{2} (x) : lo g_{2} (\frac{25}{x})

= 2 + lo g_{2} (\frac{25}{x})

- ln (\frac{x}{y})

ln (x^{3}) - ln (x)

lo g_{b} (\frac{x ^{3} y}{z ^{9}})

\frac{2}{5} ln (\frac{15}{4})

lo g_{10} (6 x)

What is 2log_{2}(10)-log_{2}(x) ?
The solution to 2log_{2}(10)-log_{2}(x) is 2+log_{2}((25)/x)