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Popular >

simplify ln(32)+ln(8)

Solution

simplify

ln (32) + ln (8)

Solution

8 ln (2)

+1

Decimal Notation

5.54517 \dots

Solution steps

ln (32) + ln (8)

Apply log rule:

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

ln (32) + ln (8) = ln (32 \cdot 8)

= ln (32 \cdot 8)

Multiply the numbers:

32 \cdot 8 = 256

= ln (256)

Rewrite

256

in power-base form:

256 = 2^{8}

= ln (2^{8})

Apply log rule:

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

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

= 8 ln (2)

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Frequently Asked Questions (FAQ)

What is ln(32)+ln(8) ?
The solution to ln(32)+ln(8) is 8ln(2)