What is 2log_{10}(a)+3log_{10}(b)-4log_{10}(c) ?

The solution to 2log_{10}(a)+3log_{10}(b)-4log_{10}(c) is log_{10}((a^2b^3)/(c^4))

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simplify 2log_{10}(a)+3log_{10}(b)-4log_{10}(c)

simplify

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

lo g_{10} (\frac{a ^{2} b ^{3}}{c ^{4}})

Solution steps

2 lo g_{10} (a) + 3 lo g_{10} (b) - 4 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) - 4 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}) - 4 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}) - 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^{2} b^{3}) - 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^{2} b^{3}) - lo g_{10} (c^{4}) = lo g_{10} (\frac{a ^{2} b ^{3}}{c ^{4}})

= lo g_{10} (\frac{a ^{2} b ^{3}}{c ^{4}})

ln (5) + ln (x - 1)

13.375 ln (\frac{x}{x - 1250})

\frac{ln ( 3 ) + ln ( 32 )}{ln ( 3 ) - ln ( 16 )}

- lo g_{10} (1.7 \cdot 1 0^{- 3})

4 lo g_{10} (4) - 2 lo g_{10} (x)

What is 2log_{10}(a)+3log_{10}(b)-4log_{10}(c) ?
The solution to 2log_{10}(a)+3log_{10}(b)-4log_{10}(c) is log_{10}((a^2b^3)/(c^4))