What is 6ln(x)+2ln(y)-4ln(z) ?

The solution to 6ln(x)+2ln(y)-4ln(z) is ln((x^6y^2)/(z^4))

Popular >

simplify 6ln(x)+2ln(y)-4ln(z)

simplify

6 ln (x) + 2 ln (y) - 4 ln (z)

ln (\frac{x ^{6} y ^{2}}{z ^{4}})

Solution steps

6 ln (x) + 2 ln (y) - 4 ln (z)

Apply log rule:

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

6 ln (x) = ln (x^{6})

= ln (x^{6}) + 2 ln (y) - 4 ln (z)

Apply log rule:

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

2 ln (y) = ln (y^{2})

= ln (x^{6}) + ln (y^{2}) - 4 ln (z)

Apply log rule:

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

ln (x^{6}) + ln (y^{2}) = ln (x^{6} y^{2})

= ln (x^{6} y^{2}) - 4 ln (z)

Apply log rule:

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

4 ln (z) = ln (z^{4})

= ln (x^{6} y^{2}) - ln (z^{4})

Apply log rule:

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

ln (x^{6} y^{2}) - ln (z^{4}) = ln (\frac{x ^{6} y ^{2}}{z ^{4}})

= ln (\frac{x ^{6} y ^{2}}{z ^{4}})

3 (ln (3) - ln (x^{2})) + (ln (x) - ln (9))

\frac{3}{16} [1 ln (1) + 4 ln (\frac{4}{3}) + 5 ln (\frac{5}{3}) + 2 ln (2)]

ln (\frac{1980 - 176}{894 - 176}) \cdot \frac{1}{3.058}

ln (x^{6} - x) - ln (x^{3} + 2)

\frac{ln ( 3 ) + ln ( h ) - ln ( 3 )}{h}

What is 6ln(x)+2ln(y)-4ln(z) ?
The solution to 6ln(x)+2ln(y)-4ln(z) is ln((x^6y^2)/(z^4))