What is expand log_{g}((sqrt(a)b^3)/(c^7)) ?

The solution to expand log_{g}((sqrt(a)b^3)/(c^7)) is log_{g}(sqrt(a))+3log_{g}(b)-7log_{g}(c)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand log_{g}((sqrt(a)b^3)/(c^7))

expand

lo g_{g} (\frac{a b ^{3}}{c ^{7}})

lo g_{g} (a) + 3 lo g_{g} (b) - 7 lo g_{g} (c)

Solution steps

lo g_{g} (\frac{a b ^{3}}{c ^{7}})

Apply log rule:

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

lo g_{g} (\frac{a b ^{3}}{c ^{7}}) = lo g_{g} (a b^{3}) - lo g_{g} (c^{7})

= lo g_{g} (b^{3} a) - lo g_{g} (c^{7})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{g} (c^{7}) = 7 lo g_{g} (c)

= lo g_{g} (a b^{3}) - 7 lo g_{g} (c)

Apply log rule:

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

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

= lo g_{g} (a) + lo g_{g} (b^{3}) - 7 lo g_{g} (c)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= lo g_{g} (a) + 3 lo g_{g} (b) - 7 lo g_{g} (c)

ln (2) \cdot \frac{2}{3}

ln (4 \cdot 4^{3})

4.18 \cdot ln (\frac{355.9}{297.38})

ln (353) - ln (343)

\frac{1}{3} lo g_{2} (x) + \frac{2}{3} lo g_{2} (y) - 3

What is expand log_{g}((sqrt(a)b^3)/(c^7)) ?
The solution to expand log_{g}((sqrt(a)b^3)/(c^7)) is log_{g}(sqrt(a))+3log_{g}(b)-7log_{g}(c)