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Popular >

simplify 4log_{e}(8)-4log_{e}(4)

Solution

simplify

4 lo g_{e} (8) - 4 lo g_{e} (4)

Solution

4 ln (2)

+1

Decimal Notation

2.77258 \dots

Solution steps

4 lo g_{e} (8) - 4 lo g_{e} (4)

Apply log rule:

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

4 lo g_{e} (8) = lo g_{e} (8^{4})

= lo g_{e} (8^{4}) - 4 lo g_{e} (4)

Apply log rule:

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

4 lo g_{e} (4) = lo g_{e} (4^{4})

= lo g_{e} (8^{4}) - lo g_{e} (4^{4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{e} (8^{4}) - lo g_{e} (4^{4}) = lo g_{e} (\frac{8 ^{4}}{4 ^{4}})

= lo g_{e} (\frac{8 ^{4}}{4 ^{4}})

\frac{8 ^{4}}{4 ^{4}} = 16

= lo g_{e} (16)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (16)

Rewrite

16

in power-base form:

16 = 2^{4}

= ln (2^{4})

Apply log rule:

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

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

= 4 ln (2)

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Frequently Asked Questions (FAQ)

What is 4log_{e}(8)-4log_{e}(4) ?
The solution to 4log_{e}(8)-4log_{e}(4) is 4ln(2)