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Popular >

simplify 5ln(2)+7ln(x)+4ln(y)

Solution

simplify

5 ln (2) + 7 ln (x) + 4 ln (y)

Solution

ln (32 x^{7} y^{4})

Solution steps

5 ln (2) + 7 ln (x) + 4 ln (y)

Apply log rule:

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

5 ln (2) = ln (2^{5})

= ln (2^{5}) + 7 ln (x) + 4 ln (y)

Apply log rule:

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

7 ln (x) = ln (x^{7})

= ln (2^{5}) + ln (x^{7}) + 4 ln (y)

Apply log rule:

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

ln (2^{5}) + ln (x^{7}) = ln (2^{5} x^{7})

= ln (2^{5} x^{7}) + 4 ln (y)

2^{5} = 32

= ln (32 x^{7}) + 4 ln (y)

Apply log rule:

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

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

= ln (32 x^{7}) + ln (y^{4})

Apply log rule:

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

ln (32 x^{7}) + ln (y^{4}) = ln (32 x^{7} y^{4})

= ln (32 x^{7} y^{4})

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Frequently Asked Questions (FAQ)

What is 5ln(2)+7ln(x)+4ln(y) ?
The solution to 5ln(2)+7ln(x)+4ln(y) is ln(32x^7y^4)