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Popular >

simplify ln(4x)-ln(x)

Solution

simplify

ln (4 x) - ln (x)

Solution

2 ln (2)

+1

Decimal Notation

1.38629 \dots

Solution steps

ln (4 x) - ln (x)

Apply log rule:

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

ln (4 x) - ln (x) = ln (\frac{4 x}{x})

= ln (\frac{4 x}{x})

Cancel the common factor:

x

= ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= ln (2^{2})

Apply log rule:

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

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

= 2 ln (2)

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Frequently Asked Questions (FAQ)

What is ln(4x)-ln(x) ?
The solution to ln(4x)-ln(x) is 2ln(2)