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Popular >

simplify ln(5*10^{12-4})

Solution

simplify

ln (5 \cdot 1 0^{12 - 4})

Solution

ln (5) + 8 ln (10)

+1

Decimal Notation

20.03011 \dots

Solution steps

ln (5 \cdot 1 0^{12 - 4})

Apply log rule:

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

ln (5 \cdot 1 0^{12 - 4}) = ln (5) + ln (1 0^{12 - 4})

= ln (5) + ln (1 0^{12 - 4})

Apply log rule:

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

ln (1 0^{12 - 4}) = (12 - 4) ln (10)

= ln (5) + (12 - 4) ln (10)

Subtract the numbers:

12 - 4 = 8

= ln (5) + 8 ln (10)

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Frequently Asked Questions (FAQ)

What is ln(5*10^{12-4}) ?
The solution to ln(5*10^{12-4}) is ln(5)+8ln(10)