What is log_{10}(x)-6log_{10}(y)+7log_{10}(z) ?

The solution to log_{10}(x)-6log_{10}(y)+7log_{10}(z) is log_{10}((xz^7)/(y^6))

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simplify log_{10}(x)-6log_{10}(y)+7log_{10}(z)

simplify

lo g_{10} (x) - 6 lo g_{10} (y) + 7 lo g_{10} (z)

lo g_{10} (\frac{x z ^{7}}{y ^{6}})

Solution steps

lo g_{10} (x) - 6 lo g_{10} (y) + 7 lo g_{10} (z)

Apply log rule:

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

6 lo g_{10} (y) = lo g_{10} (y^{6})

= lo g_{10} (x) - lo g_{10} (y^{6}) + 7 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x) - lo g_{10} (y^{6}) = lo g_{10} (\frac{x}{y ^{6}})

= lo g_{10} (\frac{x}{y ^{6}}) + 7 lo g_{10} (z)

Apply log rule:

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

7 lo g_{10} (z) = lo g_{10} (z^{7})

= lo g_{10} (\frac{x}{y ^{6}}) + lo g_{10} (z^{7})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (\frac{x}{y ^{6}}) + lo g_{10} (z^{7}) = lo g_{10} (\frac{x}{y ^{6}} z^{7})

= lo g_{10} (\frac{x}{y ^{6}} z^{7})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{10} (\frac{x z ^{7}}{y ^{6}})

ln (\frac{e ^{5}}{11})

lo g_{2} (393) - lo g_{2} (7) + 6

ln (a + b) + 5 ln (a - b) - 3 ln (c)

ln (2) + 5 ln (x) - 7 ln (y)

3 lo g_{c} (x) - \frac{1}{2} lo g_{c} (y) + 4 lo g_{c} (w)

What is log_{10}(x)-6log_{10}(y)+7log_{10}(z) ?
The solution to log_{10}(x)-6log_{10}(y)+7log_{10}(z) is log_{10}((xz^7)/(y^6))