What is 2log_{10}(x)-3log_{10}(y) ?

The solution to 2log_{10}(x)-3log_{10}(y) is log_{10}((x^2)/(y^3))

Popular >

simplify 2log_{10}(x)-3log_{10}(y)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

lo g_{10} (\frac{y ^{7}}{x z ^{3}})

3 ln (x) + 5 ln (y) - 6 ln (z)

lo g_{3} (4) + 2 lo g_{3} (5)

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

ln (y) - ln (x)

What is 2log_{10}(x)-3log_{10}(y) ?
The solution to 2log_{10}(x)-3log_{10}(y) is log_{10}((x^2)/(y^3))