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Popular >

simplify 3ln(4)+ln(2^5)

Solution

simplify

3 ln (4) + ln (2^{5})

Solution

11 ln (2)

+1

Decimal Notation

7.62461 \dots

Solution steps

3 ln (4) + ln (2^{5})

Apply log rule:

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

3 ln (4) = ln (4^{3})

= ln (4^{3}) + ln (2^{5})

Apply log rule:

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

ln (4^{3}) + ln (2^{5}) = ln (2^{5} \cdot 4^{3})

= ln (2^{5} \cdot 4^{3})

4^{3} \cdot 2^{5} = 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 3ln(4)+ln(2^5) ?
The solution to 3ln(4)+ln(2^5) is 11ln(2)