What is ln((4.08*10^{22})/(5*10^{22)}) ?

The solution to ln((4.08*10^{22})/(5*10^{22)}) is -ln(5)+ln(4.08)

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simplify ln((4.0810^{22})/(510^{22)})

simplify

ln (\frac{4.08 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}})

- ln (5) + ln (4.08)

Decimal Notation

- 0.20334 \dots

Solution steps

ln (\frac{4.08 \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{4.08 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}}) = ln (4.08 \cdot 1 0^{22}) - ln (5 \cdot 1 0^{22})

= ln (1 0^{22} \cdot 4.08) - ln (1 0^{22} \cdot 5)

Apply log rule:

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

ln (4.08 \cdot 1 0^{22}) = ln (4.08) + ln (1 0^{22}), ln (5 \cdot 1 0^{22}) = ln (5) + ln (1 0^{22})

= ln (4.08) + 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 (4.08) + 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 (4.08) + 22 ln (10) - (ln (5) + 22 ln (10))

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

= ln (4.08) + 22 ln (10) - ln (5) - 22 ln (10)

Simplify

ln (4.08) + 22 ln (10) - ln (5) - 22 ln (10) : - ln (5) + ln (4.08)

= - ln (5) + ln (4.08)

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

- \frac{ln ( 6 )}{4 ln ( 2 )}

- 0.77 - \frac{0.591}{3} \cdot lo g_{10} (\frac{0.001}{0.1})

ln (x^{- 1}) + 2 ln (x)

ln (v) + 5 ln (x)

What is ln((4.08*10^{22})/(5*10^{22)}) ?
The solution to ln((4.08*10^{22})/(5*10^{22)}) is -ln(5)+ln(4.08)