What is 3log_{10}(a)+5log_{10}(b)-4log_{10}(c) ?

The solution to 3log_{10}(a)+5log_{10}(b)-4log_{10}(c) is log_{10}((a^3b^5)/(c^4))

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simplify 3log_{10}(a)+5log_{10}(b)-4log_{10}(c)

simplify

3 lo g_{10} (a) + 5 lo g_{10} (b) - 4 lo g_{10} (c)

lo g_{10} (\frac{a ^{3} b ^{5}}{c ^{4}})

Solution steps

3 lo g_{10} (a) + 5 lo g_{10} (b) - 4 lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a^{3}) + 5 lo g_{10} (b) - 4 lo g_{10} (c)

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^{3}) + lo g_{10} (b^{5}) - 4 lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a^{3} b^{5}) - 4 lo g_{10} (c)

Apply log rule:

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

4 lo g_{10} (c) = lo g_{10} (c^{4})

= lo g_{10} (a^{3} b^{5}) - lo g_{10} (c^{4})

Apply log rule:

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

lo g_{10} (a^{3} b^{5}) - lo g_{10} (c^{4}) = lo g_{10} (\frac{a ^{3} b ^{5}}{c ^{4}})

= lo g_{10} (\frac{a ^{3} b ^{5}}{c ^{4}})

lo g_{b} (x - 1) + lo g_{b} (3)

lo g_{10} (mn)

- (\frac{1}{4}) lo g_{2} (\frac{1}{4}) - (\frac{3}{4}) lo g_{2} (\frac{3}{4})

lo g_{2} (x^{2} y)

lo g_{4} (5 x y)

What is 3log_{10}(a)+5log_{10}(b)-4log_{10}(c) ?
The solution to 3log_{10}(a)+5log_{10}(b)-4log_{10}(c) is log_{10}((a^3b^5)/(c^4))