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Popular >

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

Solution

simplify

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

Solution

9 ln (2)

+1

Decimal Notation

6.23832 \dots

Solution steps

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

Apply log rule:

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

2 ln (4) = ln (4^{2})

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

Apply log rule:

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

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

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

4^{2} \cdot 2^{5} = 512

= ln (512)

Rewrite

512

in power-base form:

512 = 2^{9}

= ln (2^{9})

Apply log rule:

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

ln (2^{9}) = 9 ln (2)

= 9 ln (2)

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Frequently Asked Questions (FAQ)

What is 2ln(4)+ln(2^5) ?
The solution to 2ln(4)+ln(2^5) is 9ln(2)