Question

g Use the properties of the natural logarithm to rewrite each logarithmic expression as an expression with a single logarithm. a . ln ( x + 5 ) − ln ( x − 5 ) = b . ln ( x + 5 ) + ln ( x − 5 )

Answer 1

Answer:

Given:

(a.) ㏑( x + 5 ) − ㏑( x − 5 )

(b.) ㏑( x + 5 ) + ㏑( x − 5 )

To compute the above expression, we'll use the properties of natural logarithm. i.e.

㏑(a) − ㏑(b) =  ㏑$\frac{a}{b}$

∴ ㏑( x + 5 ) − ㏑( x − 5 ) = ㏑$\frac{x+5}{x-5}$

Similarly

㏑(a) + ㏑(b) =  ㏑$(a\times b)$

∴ ㏑( x + 5 ) + ㏑( x − 5 ) = ㏑($x^{2}$-25)