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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

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

Solution steps

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

2 ln (5 x + 3) - 5 ln (x - 3) - 4 ln (x)

ln (6) + (ln (4) - ln (3))

\frac{1}{2} lo g_{b} (x) + 5 lo g_{b} (y) - 2 lo g_{b} (x)

lo g_{10} (3) + lo g_{10} (x)

lo g_{3} (\frac{x y ^{2}}{z ^{2}})

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