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Popular >

simplify ln(8)+4ln(4)

Solution

simplify

ln (8) + 4 ln (4)

Solution

11 ln (2)

+1

Solution steps

ln (8) + 4 ln (4)

Apply log rule:

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

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

= ln (8) + ln (4^{4})

Apply log rule:

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

ln (8) + ln (4^{4}) = ln (4^{4} \cdot 8)

= ln (4^{4} \cdot 8)

8 \cdot 4^{4} = 2048

= ln (2048)

Rewrite

2048

in power-base form:

2048 = 2^{11}

= ln (2^{11})

Apply log rule:

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

ln (2^{11}) = 11 ln (2)

= 11 ln (2)

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Frequently Asked Questions (FAQ)

What is ln(8)+4ln(4) ?
The solution to ln(8)+4ln(4) is 11ln(2)