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Popular >

simplify 2*ln(9)+ln(4)

Solution

simplify

2 \cdot ln (9) + ln (4)

Solution

2 ln (18)

+1

Decimal Notation

5.78074 \dots

Solution steps

2 ln (9) + ln (4)

Apply log rule:

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

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

= ln (9^{2}) + ln (4)

Apply log rule:

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

ln (9^{2}) + ln (4) = ln (9^{2} \cdot 4)

= ln (9^{2} \cdot 4)

9^{2} \cdot 4 = 324

= ln (324)

Rewrite

324

in power-base form:

324 = 1 8^{2}

= ln (1 8^{2})

Apply log rule:

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

ln (1 8^{2}) = 2 ln (18)

= 2 ln (18)

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Frequently Asked Questions (FAQ)

What is 2*ln(9)+ln(4) ?
The solution to 2*ln(9)+ln(4) is 2ln(18)