write the expression as a single logarithm (1)/(4)in x+5[in(x-2)-(3)/(10)in(x+2)]
To write the expression as a single logarithm, we can use the properties of logarithms.
Using the property log(base a) (b) + log(base a) (c) = log(base a) (b * c), we can simplify the expression:
(1/4) * ln(x+5) + ln(x-2) - (3/10) * ln(x+2)
Combining the first two terms:
(1/4) * ln(x+5) + ln(x-2) becomes ln((x+5)^(1/4) * (x-2))
So, the expression becomes:
ln((x+5)^(1/4) * (x-2)) - (3/10) * ln(x+2)