What is 2log_{5}(3x)-log_{5}(5x) ?

The solution to 2log_{5}(3x)-log_{5}(5x) is log_{5}((9x)/5)

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simplify 2log_{5}(3x)-log_{5}(5x)

simplify

2 lo g_{5} (3 x) - lo g_{5} (5 x)

lo g_{5} (\frac{9 x}{5})

Solution steps

2 lo g_{5} (3 x) - lo g_{5} (5 x)

Apply log rule:

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

2 lo g_{5} (3 x) = lo g_{5} ((3 x)^{2})

= lo g_{5} ((3 x)^{2}) - lo g_{5} (5 x)

Apply log rule:

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

lo g_{5} ((3 x)^{2}) - lo g_{5} (5 x) = lo g_{5} (\frac{( 3 x ) ^{2}}{5 x})

= lo g_{5} (\frac{( 3 x ) ^{2}}{5 x})

Simplify

\frac{( 3 x ) ^{2}}{5 x} : \frac{9 x}{5}

= lo g_{5} (\frac{9 x}{5})

3 ln (x) + 5 ln (3)

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

34 lo g_{2} (a) - 13 lo g_{2} (b) + 5 lo g_{2} (c)

ln (3 \cdot 1 0^{14})

What is 2log_{5}(3x)-log_{5}(5x) ?
The solution to 2log_{5}(3x)-log_{5}(5x) is log_{5}((9x)/5)