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Popular >

simplify 10ln(10)-10ln(5)

Solution

simplify

10 ln (10) - 10 ln (5)

Solution

10 ln (2)

+1

Decimal Notation

6.93147 \dots

Solution steps

10 ln (10) - 10 ln (5)

Apply log rule:

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

10 ln (10) = ln (1 0^{10})

= ln (1 0^{10}) - 10 ln (5)

Apply log rule:

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

10 ln (5) = ln (5^{10})

= ln (1 0^{10}) - ln (5^{10})

Apply log rule:

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

ln (1 0^{10}) - ln (5^{10}) = ln (\frac{1 0 ^{10}}{5 ^{10}})

= ln (\frac{1 0 ^{10}}{5 ^{10}})

\frac{1 0 ^{10}}{5 ^{10}} = 1024

= ln (1024)

Rewrite

1024

in power-base form:

1024 = 2^{10}

= ln (2^{10})

Apply log rule:

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

ln (2^{10}) = 10 ln (2)

= 10 ln (2)

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Frequently Asked Questions (FAQ)

What is 10ln(10)-10ln(5) ?
The solution to 10ln(10)-10ln(5) is 10ln(2)