What is 2log_{10}(a)+3log_{10}(b)-5log_{10}(c) ?

The solution to 2log_{10}(a)+3log_{10}(b)-5log_{10}(c) is log_{10}((a^2b^3)/(c^5))

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simplify 2log_{10}(a)+3log_{10}(b)-5log_{10}(c)

simplify

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

lo g_{10} (\frac{a ^{2} b ^{3}}{c ^{5}})

Solution steps

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

Apply log rule:

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

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

= lo g_{10} (a^{2}) + 3 lo g_{10} (b) - 5 lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a^{2}) + lo g_{10} (b^{3}) - 5 lo g_{10} (c)

Apply log rule:

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

lo g_{10} (a^{2}) + lo g_{10} (b^{3}) = lo g_{10} (a^{2} b^{3})

= lo g_{10} (a^{2} b^{3}) - 5 lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a^{2} b^{3}) - lo g_{10} (c^{5})

Apply log rule:

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

lo g_{10} (a^{2} b^{3}) - lo g_{10} (c^{5}) = lo g_{10} (\frac{a ^{2} b ^{3}}{c ^{5}})

= lo g_{10} (\frac{a ^{2} b ^{3}}{c ^{5}})

ln (60 e^{- 8.064})

ln (\frac{7.28 \cdot 1 0 ^{- 4}}{1.93 \cdot 1 0 ^{- 7}})

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

\frac{1}{3} lo g_{10} (27) - \frac{1}{2} lo g_{10} (49)

ln ((2) e^{7 b})

What is 2log_{10}(a)+3log_{10}(b)-5log_{10}(c) ?
The solution to 2log_{10}(a)+3log_{10}(b)-5log_{10}(c) is log_{10}((a^2b^3)/(c^5))