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

The solution to 2log_{10}(y)+3(log_{10}(w)-3log_{10}(x)) is log_{10}((y^2w^3)/(x^9))

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

simplify

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

lo g_{10} (\frac{y ^{2} w ^{3}}{x ^{9}})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

y^{2} (\frac{w}{x ^{3}})^{3} : \frac{y ^{2} w ^{3}}{x ^{9}}

= lo g_{10} (\frac{y ^{2} w ^{3}}{x ^{9}})

7 lo g_{m} (w) - \frac{1}{3} lo g_{m} (z) + 6 lo g_{m} (x)

ln (x) + \frac{1}{2} ln (1 + \frac{2 y}{x})

85 + 10 lo g_{10} (\frac{2.5}{8})

6.1 - lo g_{10} (\frac{51}{18.5})

\frac{1}{4} ln (3 x + 1) - \frac{1}{4} ln (x - 1) + ln (k)

What is 2log_{10}(y)+3(log_{10}(w)-3log_{10}(x)) ?
The solution to 2log_{10}(y)+3(log_{10}(w)-3log_{10}(x)) is log_{10}((y^2w^3)/(x^9))