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Popular >

simplify ln((1.011*10^4)/1)

Solution

simplify

ln (\frac{1.011 \cdot 1 0 ^{4}}{1})

Solution

4 ln (10) + ln (1.011)

+1

Decimal Notation

9.22128 \dots

Solution steps

ln (\frac{1.011 \cdot 1 0 ^{4}}{1})

Apply log rule:

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

ln (\frac{1.011 \cdot 1 0 ^{4}}{1}) = ln (1.011 \cdot 1 0^{4}) - ln (1)

= ln (1 0^{4} \cdot 1.011) - ln (1)

Apply log rule:

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

ln (1.011 \cdot 1 0^{4}) = ln (1.011) + ln (1 0^{4})

= ln (1.011) + ln (1 0^{4}) - ln (1)

Apply log rule:

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

ln (1 0^{4}) = 4 ln (10)

= ln (1.011) + 4 ln (10) - ln (1)

Apply log rule:

lo g_{a} (1) = 0

= ln (1.011) + 4 ln (10) - 0

ln (1.011) + 4 ln (10) - 0 = ln (1.011) + 4 ln (10)

= 4 ln (10) + ln (1.011)

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Frequently Asked Questions (FAQ)

What is ln((1.011*10^4)/1) ?
The solution to ln((1.011*10^4)/1) is 4ln(10)+ln(1.011)