What is ln((12*10^6)/(1*10^8)) ?

The solution to ln((12*10^6)/(1*10^8)) is ln(12)-2ln(10)

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simplify ln((1210^6)/(110^8))

simplify

ln (\frac{12 \cdot 1 0 ^{6}}{1 \cdot 1 0 ^{8}})

ln (12) - 2 ln (10)

Decimal Notation

- 2.12026 \dots

Solution steps

ln (\frac{12 \cdot 1 0 ^{6}}{1 \cdot 1 0 ^{8}})

Apply log rule:

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

ln (\frac{12 \cdot 1 0 ^{6}}{1 \cdot 1 0 ^{8}}) = ln (12 \cdot 1 0^{6}) - ln (1 \cdot 1 0^{8})

= ln (1 0^{6} \cdot 12) - ln (1 0^{8} \cdot 1)

Apply log rule:

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

ln (12 \cdot 1 0^{6}) = ln (12) + ln (1 0^{6}), ln (1 \cdot 1 0^{8}) = ln (1) + ln (1 0^{8})

= ln (12) + ln (1 0^{6}) - (ln (1) + ln (1 0^{8}))

Apply log rule:

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

ln (1 0^{6}) = 6 ln (10)

= ln (12) + 6 ln (10) - (ln (1) + ln (1 0^{8}))

Apply log rule:

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

ln (1 0^{8}) = 8 ln (10)

= ln (12) + 6 ln (10) - (ln (1) + 8 ln (10))

- (ln (1) + 8 ln (10)) = - 8 ln (10)

= ln (12) + 6 ln (10) - 8 ln (10)

Add similar elements:

6 ln (10) - 8 ln (10) = - 2 ln (10)

= ln (12) - 2 ln (10)

1 + ln (\frac{1}{2})

ln (3.8 2.2 x + 5.4)

5 ln (\frac{5}{3})

ln ((x + 1)^{2} \frac{d y}{d x})

What is ln((12*10^6)/(1*10^8)) ?
The solution to ln((12*10^6)/(1*10^8)) is ln(12)-2ln(10)