What is simplify-ln(10)+ln(5) ?

The solution to simplify-ln(10)+ln(5) is -ln(2)

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simplify-ln(10)+ln(5)

simplify

- ln (10) + ln (5)

- ln (2)

Decimal

- 0.69314 \dots

Solution steps

- ln (10) + ln (5)

Apply log rule:

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

ln (5) - ln (10) = ln (\frac{5}{10})

= ln (\frac{5}{10})

Cancel the common factor:

5

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

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (2)

ln (\frac{3 x - 2 y}{2 x + 2 y})

- lo g_{10} (1.58 \cdot 1 0^{- 5})

ln (\frac{e ^{x^{2}} \cdot cos ( x )}{2 x + 4})

ln (\frac{\frac{π}{4} \cdot 4 7 ^{2}}{\frac{π}{4} \cdot 3 0 ^{2}})

lo g_{10} (x^{9} z)