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

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

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

simplify

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

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

Solution steps

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

Apply the distributive law:

- (a + b) = - a - b

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

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

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

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

Simplify

\frac{\frac{c ^{2}}{a ^{3}}}{b} : \frac{c ^{2}}{a ^{3} b}

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

10 lo g_{10} (1 0^{12} I)

lo g_{99} (\frac{9}{23}) + lo g_{99} (\frac{23}{9})

ln (\frac{x}{x + 6})

ln (3) - 2 ln (4) + ln (32)

\frac{ln ( \frac{3}{20} )}{4 ln ( 2 )}

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