What is log_{10}(a)+3log_{10}(c)-5log_{10}(b) ?

The solution to log_{10}(a)+3log_{10}(c)-5log_{10}(b) is log_{10}((ac^3)/(b^5))

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simplify log_{10}(a)+3log_{10}(c)-5log_{10}(b)

simplify

lo g_{10} (a) + 3 lo g_{10} (c) - 5 lo g_{10} (b)

lo g_{10} (\frac{a c ^{3}}{b ^{5}})

Solution steps

lo g_{10} (a) + 3 lo g_{10} (c) - 5 lo g_{10} (b)

Apply log rule:

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

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

= lo g_{10} (a) + lo g_{10} (c^{3}) - 5 lo g_{10} (b)

Apply log rule:

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

lo g_{10} (a) + lo g_{10} (c^{3}) = lo g_{10} (a c^{3})

= lo g_{10} (a c^{3}) - 5 lo g_{10} (b)

Apply log rule:

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

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

= lo g_{10} (a c^{3}) - lo g_{10} (b^{5})

Apply log rule:

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

lo g_{10} (a c^{3}) - lo g_{10} (b^{5}) = lo g_{10} (\frac{a c ^{3}}{b ^{5}})

= lo g_{10} (\frac{a c ^{3}}{b ^{5}})

ln (v) - ln ∣ x - 1 ∣ + 2 ln ∣ x ∣

ln (\frac{( x - 1 )}{x + 1})

ln (\frac{0.5}{0.375})

ln (\frac{x}{3})

6 lo g_{2} (x) + lo g_{2} (y)

What is log_{10}(a)+3log_{10}(c)-5log_{10}(b) ?
The solution to log_{10}(a)+3log_{10}(c)-5log_{10}(b) is log_{10}((ac^3)/(b^5))