What is ln((4.67*10^{22})/(5*10^{22)}) ?

The solution to ln((4.67*10^{22})/(5*10^{22)}) is -ln(5)+ln(4.67)

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simplify ln((4.6710^{22})/(510^{22)})

simplify

ln (\frac{4.67 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}})

- ln (5) + ln (4.67)

Decimal Notation

- 0.06827 \dots

Solution steps

ln (\frac{4.67 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}})

Apply log rule:

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

ln (\frac{4.67 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}}) = ln (4.67 \cdot 1 0^{22}) - ln (5 \cdot 1 0^{22})

= ln (1 0^{22} \cdot 4.67) - ln (1 0^{22} \cdot 5)

Apply log rule:

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

ln (4.67 \cdot 1 0^{22}) = ln (4.67) + ln (1 0^{22}), ln (5 \cdot 1 0^{22}) = ln (5) + ln (1 0^{22})

= ln (4.67) + ln (1 0^{22}) - (ln (5) + ln (1 0^{22}))

Apply log rule:

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

ln (1 0^{22}) = 22 ln (10)

= ln (4.67) + 22 ln (10) - (ln (5) + 22 ln (10))

Apply log rule:

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

ln (1 0^{22}) = 22 ln (10)

= ln (4.67) + 22 ln (10) - (ln (5) + 22 ln (10))

- (ln (5) + 22 ln (10)) : - ln (5) - 22 ln (10)

= ln (4.67) + 22 ln (10) - ln (5) - 22 ln (10)

Simplify

ln (4.67) + 22 ln (10) - ln (5) - 22 ln (10) : - ln (5) + ln (4.67)

= - ln (5) + ln (4.67)

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What is ln((4.67*10^{22})/(5*10^{22)}) ?
The solution to ln((4.67*10^{22})/(5*10^{22)}) is -ln(5)+ln(4.67)