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Popular >

simplify 4ln(x)+6ln(y)+3ln(z)

Solution

simplify

4 ln (x) + 6 ln (y) + 3 ln (z)

Solution

ln (x^{4} y^{6} z^{3})

Solution steps

4 ln (x) + 6 ln (y) + 3 ln (z)

Apply log rule:

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

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

= ln (x^{4}) + 6 ln (y) + 3 ln (z)

Apply log rule:

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

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

= ln (x^{4}) + ln (y^{6}) + 3 ln (z)

Apply log rule:

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

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

= ln (x^{4} y^{6}) + 3 ln (z)

Apply log rule:

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

3 ln (z) = ln (z^{3})

= ln (x^{4} y^{6}) + ln (z^{3})

Apply log rule:

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

ln (x^{4} y^{6}) + ln (z^{3}) = ln (x^{4} y^{6} z^{3})

= ln (x^{4} y^{6} z^{3})

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Frequently Asked Questions (FAQ)

What is 4ln(x)+6ln(y)+3ln(z) ?
The solution to 4ln(x)+6ln(y)+3ln(z) is ln(x^4y^6z^3)