What is ln(10^510^{-3}) ?

The solution to ln(10^510^{-3}) is 2ln(10)

Popular >

simplify ln(10^510^{-3})

simplify

ln (1 0^{5} 1 0^{- 3})

2 ln (10)

Decimal Notation

4.60517 \dots

Solution steps

ln (1 0^{5} \cdot 1 0^{- 3})

Apply log rule:

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

ln (1 0^{5} \cdot 1 0^{- 3}) = ln (1 0^{5}) + ln (1 0^{- 3})

= ln (1 0^{5}) + ln (1 0^{- 3})

Apply log rule:

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

ln (1 0^{5}) = 5 ln (10)

= 5 ln (10) + ln (1 0^{- 3})

Apply log rule:

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

ln (1 0^{- 3}) = - 3 ln (10)

= 5 ln (10) - 3 ln (10)

Add similar elements:

5 ln (10) - 3 ln (10) = 2 ln (10)

= 2 ln (10)

\frac{ln ( 10000 ) - ln ( 1000 )}{0.0525}

7 ln (x y) - 4 ln (yz)

ln (10) - ln (9)

lo g_{2} (\frac{x + y}{( x - y ) ^{4}})

lo g_{3} (\frac{x ^{4}}{3 y ^{3}})