What is log_{5}(7x)+2log_{5}(3)-log_{5}(8) ?

The solution to log_{5}(7x)+2log_{5}(3)-log_{5}(8) is log_{5}((63x)/8)

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simplify log_{5}(7x)+2log_{5}(3)-log_{5}(8)

simplify

lo g_{5} (7 x) + 2 lo g_{5} (3) - lo g_{5} (8)

lo g_{5} (\frac{63 x}{8})

Solution steps

lo g_{5} (7 x) + 2 lo g_{5} (3) - lo g_{5} (8)

Apply log rule:

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

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

= lo g_{5} (7 x) + lo g_{5} (3^{2}) - lo g_{5} (8)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{5} (7 x) + lo g_{5} (3^{2}) = lo g_{5} (7 x \cdot 3^{2})

= lo g_{5} (7 x \cdot 3^{2}) - lo g_{5} (8)

Apply log rule:

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

lo g_{5} (7 x \cdot 3^{2}) - lo g_{5} (8) = lo g_{5} (\frac{7 x \cdot 3 ^{2}}{8})

= lo g_{5} (\frac{7 x \cdot 3 ^{2}}{8})

Simplify

7 x \cdot 3^{2} : 63 x

= lo g_{5} (\frac{63 x}{8})

lo g_{6} (x y z^{4})

lo g_{10} (\frac{x ^{m} y ^{n}}{2 x ^{3} y})

lo g_{10} (\frac{1000000}{x ^{2} + y ^{2}})

ln (x^{10} 6 - x)

lo g_{2} (15) + 6 lo g_{2} (x) - \frac{4}{3} lo g_{2} (x)

What is log_{5}(7x)+2log_{5}(3)-log_{5}(8) ?
The solution to log_{5}(7x)+2log_{5}(3)-log_{5}(8) is log_{5}((63x)/8)