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Popular >

simplify 2log_{e}(4)+2log_{e}(5)

Solution

simplify

2 lo g_{e} (4) + 2 lo g_{e} (5)

Solution

2 ln (20)

+1

Decimal Notation

5.99146 \dots

Solution steps

2 lo g_{e} (4) + 2 lo g_{e} (5)

Apply log rule:

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

2 lo g_{e} (4) = lo g_{e} (4^{2})

= lo g_{e} (4^{2}) + 2 lo g_{e} (5)

Apply log rule:

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

2 lo g_{e} (5) = lo g_{e} (5^{2})

= lo g_{e} (4^{2}) + lo g_{e} (5^{2})

Apply log rule:

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

lo g_{e} (4^{2}) + lo g_{e} (5^{2}) = lo g_{e} (4^{2} \cdot 5^{2})

= lo g_{e} (4^{2} \cdot 5^{2})

4^{2} \cdot 5^{2} = 400

= lo g_{e} (400)

Apply log rule:

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

= ln (400)

Rewrite

400

in power-base form:

400 = 2 0^{2}

= ln (2 0^{2})

Apply log rule:

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

ln (2 0^{2}) = 2 ln (20)

= 2 ln (20)

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lo g_{3} (\frac{7}{13})

Frequently Asked Questions (FAQ)

What is 2log_{e}(4)+2log_{e}(5) ?
The solution to 2log_{e}(4)+2log_{e}(5) is 2ln(20)