What is 5log_{10}(x)-(3log_{10}(y)+log_{10}(z)) ?

The solution to 5log_{10}(x)-(3log_{10}(y)+log_{10}(z)) is log_{10}((x^5)/(y^3z))

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simplify 5log_{10}(x)-(3log_{10}(y)+log_{10}(z))

simplify

5 lo g_{10} (x) - (3 lo g_{10} (y) + lo g_{10} (z))

lo g_{10} (\frac{x ^{5}}{y ^{3} z})

Solution steps

5 lo g_{10} (x) - (3 lo g_{10} (y) + lo g_{10} (z))

Apply the distributive law:

- (a + b) = - a - b

- (3 lo g_{10} (y) + lo g_{10} (z)) = - 3 lo g_{10} (y) - lo g_{10} (z)

= 5 lo g_{10} (x) - 3 lo g_{10} (y) - lo g_{10} (z)

5 lo g_{10} (x) = lo g_{10} (x^{5})

- 3 lo g_{10} (y) = - lo g_{10} (y^{3})

= lo g_{10} (x^{5}) - lo g_{10} (y^{3}) - lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{5}) - lo g_{10} (y^{3}) = lo g_{10} (\frac{x ^{5}}{y ^{3}})

= lo g_{10} (\frac{x ^{5}}{y ^{3}}) - lo g_{10} (z)

Apply log rule:

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

lo g_{10} (\frac{x ^{5}}{y ^{3}}) - lo g_{10} (z) = lo g_{10} (\frac{\frac{x ^{5}}{y ^{3}}}{z})

= lo g_{10} (\frac{\frac{x ^{5}}{y ^{3}}}{z})

Simplify

\frac{\frac{x ^{5}}{y ^{3}}}{z} : \frac{x ^{5}}{y ^{3} z}

= lo g_{10} (\frac{x ^{5}}{y ^{3} z})

ln (\frac{13}{200})

ln (x x^{2} - 6)

2 ln (3) - ln (4)

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

\frac{ln ( 5 ) - 2 ln ( 2 )}{ln ( 3 ) - ln ( 2 )}

What is 5log_{10}(x)-(3log_{10}(y)+log_{10}(z)) ?
The solution to 5log_{10}(x)-(3log_{10}(y)+log_{10}(z)) is log_{10}((x^5)/(y^3z))