What is 4log_{10}(x)-2log_{10}(y)+3log_{10}(z) ?

The solution to 4log_{10}(x)-2log_{10}(y)+3log_{10}(z) is log_{10}((x^4z^3)/(y^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4log_{10}(x)-2log_{10}(y)+3log_{10}(z)

simplify

4 lo g_{10} (x) - 2 lo g_{10} (y) + 3 lo g_{10} (z)

lo g_{10} (\frac{x ^{4} z ^{3}}{y ^{2}})

Solution steps

4 lo g_{10} (x) - 2 lo g_{10} (y) + 3 lo g_{10} (z)

Apply log rule:

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

4 lo g_{10} (x) = lo g_{10} (x^{4})

= lo g_{10} (x^{4}) - 2 lo g_{10} (y) + 3 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{4}) - lo g_{10} (y^{2}) + 3 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{4}) - lo g_{10} (y^{2}) = lo g_{10} (\frac{x ^{4}}{y ^{2}})

= lo g_{10} (\frac{x ^{4}}{y ^{2}}) + 3 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (\frac{x ^{4}}{y ^{2}}) + lo g_{10} (z^{3})

Apply log rule:

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

lo g_{10} (\frac{x ^{4}}{y ^{2}}) + lo g_{10} (z^{3}) = lo g_{10} (\frac{x ^{4}}{y ^{2}} z^{3})

= lo g_{10} (\frac{x ^{4}}{y ^{2}} z^{3})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{10} (\frac{x ^{4} z ^{3}}{y ^{2}})

\frac{1}{3} (lo g_{8} (a) + 2 lo g_{8} (b))

ln (\frac{( 1.6 \cdot 1 0 ^{- 19} )}{( 6.48 \cdot 1 0 ^{- 5} )})

lo g_{10} (2) + \frac{1}{2} \cdot lo g_{10} (15) - \frac{1}{4} \cdot lo g_{10} (9)

lo g_{b} (x^{7} y^{3} z)

- 2 ln ∣ 4 - 1 ∣ + 3 ln ∣ 4 - 2 ∣ + ln 4^{2} + 1 + 2 - ln (\frac{5}{2})

What is 4log_{10}(x)-2log_{10}(y)+3log_{10}(z) ?
The solution to 4log_{10}(x)-2log_{10}(y)+3log_{10}(z) is log_{10}((x^4z^3)/(y^2))