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Popular >

simplify ln(2)+2ln(sqrt(2))

Solution

simplify

ln (2) + 2 ln (2)

Solution

2 ln (2)

+1

Decimal Notation

1.38629 \dots

Solution steps

ln (2) + 2 ln (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 (2)^{2} = 4

= ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= ln (2^{2})

Apply log rule:

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

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

= 2 ln (2)

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Frequently Asked Questions (FAQ)

What is ln(2)+2ln(sqrt(2)) ?
The solution to ln(2)+2ln(sqrt(2)) is 2ln(2)