Respuesta :
Answer:
ln15 or ≈ 2.708
Step-by-step explanation:
we can use the rules of logarithms to condense the logarithm
ln10 - ln2 + ln3
looking at the expression from left to right we see the first 2 terms: ln10 - ln2
we can use the quotient rule where log base b (x/y) = log base b x - log base b y. in other words, the quotient rule allows us to write a subtraction of 2 logarithims with the same base as a division
ln10 and ln2 have the same base e, so we can write them as a division
[tex]\frac{ln10}{ln2}[/tex]
so we have the expression: [tex]\frac{ln10}{ln2}[/tex] + ln3
we can simplify [tex]\frac{ln10}{ln2}[/tex] to equal ln5, as 10/2 = 5
the new expression is ln5 + ln3
next, we can use the product rule where log base b (x)(y) = log base b x + log base b y. in other words, 2 logarithims with the same base added together can be written as a multiplication
ln5 and ln3 have the same base, so we will write them as a multiplication
(ln5)(ln3) = ln15
our final answer is ln15, which can be simplified if needed in decimal form as ≈ 2.708
