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Popular >

simplify ln(8)+ln(4)

Solution

simplify

ln (8) + ln (4)

Solution

5 ln (2)

+1

Decimal Notation

3.46573 \dots

Solution steps

ln (8) + ln (4)

Apply log rule:

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

ln (8) + ln (4) = ln (8 \cdot 4)

= ln (8 \cdot 4)

Multiply the numbers:

8 \cdot 4 = 32

= ln (32)

Rewrite

32

in power-base form:

32 = 2^{5}

= ln (2^{5})

Apply log rule:

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

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

= 5 ln (2)

Popular Examples

simplify log_{1/2}(8x)simplify

lo g_{\frac{1}{2}} (8 x)

expand log_{10}((x^2)/3)expand

lo g_{10} (\frac{x ^{2}}{3})

simplify ln(x)-1/2 ln(x^2+1)simplify

ln (x) - \frac{1}{2} ln (x^{2} + 1)

simplify ln(sqrt(ab))+ln(a/e)simplify

ln (ab) + ln (\frac{a}{e})

expand log_{2}(x^5)expand

lo g_{2} (x^{5})

Frequently Asked Questions (FAQ)

What is ln(8)+ln(4) ?
The solution to ln(8)+ln(4) is 5ln(2)