What is log_{10}(8)+log_{10}(x)-2log_{10}(x+4) ?

The solution to log_{10}(8)+log_{10}(x)-2log_{10}(x+4) is log_{10}((8x)/((x+4)^2))

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simplify log_{10}(8)+log_{10}(x)-2log_{10}(x+4)

simplify

lo g_{10} (8) + lo g_{10} (x) - 2 lo g_{10} (x + 4)

lo g_{10} (\frac{8 x}{( x + 4 ) ^{2}})

Solution steps

lo g_{10} (8) + lo g_{10} (x) - 2 lo g_{10} (x + 4)

lo g_{10} (8) = 3 lo g_{10} (2)

= 3 lo g_{10} (2) + lo g_{10} (x) - 2 lo g_{10} (x + 4)

3 lo g_{10} (2) = lo g_{10} (2^{3})

- 2 lo g_{10} (x + 4) = - lo g_{10} ((x + 4)^{2})

= lo g_{10} (2^{3}) + lo g_{10} (x) - lo g_{10} ((x + 4)^{2})

Apply log rule:

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

lo g_{10} (2^{3}) + lo g_{10} (x) = lo g_{10} (2^{3} x)

= lo g_{10} (2^{3} x) - lo g_{10} ((x + 4)^{2})

Apply log rule:

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

lo g_{10} (2^{3} x) - lo g_{10} ((x + 4)^{2}) = lo g_{10} (\frac{2 ^{3} x}{( x + 4 ) ^{2}})

= lo g_{10} (\frac{2 ^{3} x}{( x + 4 ) ^{2}})

Simplify

\frac{2 ^{3} x}{( x + 4 ) ^{2}} : \frac{8 x}{( x + 4 ) ^{2}}

= lo g_{10} (\frac{8 x}{( x + 4 ) ^{2}})

lo g_{10} (2 x) + lo g_{10} (50 y)

lo g_{2} (x y)

lo g_{6} (\frac{c}{36})

lo g_{10} (\frac{x ( x + 6 )}{( x + 5 ) ^{6}})

lo g_{5} (\frac{x}{x + 2})

What is log_{10}(8)+log_{10}(x)-2log_{10}(x+4) ?
The solution to log_{10}(8)+log_{10}(x)-2log_{10}(x+4) is log_{10}((8x)/((x+4)^2))