Question

Use properties of logs to simplify the ex-
pression
log4(x −square root (x2 − 28 )) + log4(x + square root (x2 − 28 )).

So the property logs for addition is log base b (xy) so I did log base 4 (x-square root of (x^2-28))(logbase4(x+square root of (x^2-28))

Am I supposed to foil this out? Is there a better way of understanding this problem?

Answer 1

\[\log_{n}x+\log_{n}x=2\log_{n}x \]

Answer 2

\[=\log_{n}x^2\]

Answer 3

both logs given are different...I am just confused

Answer 4

It's difference between two squares.

Answer 5

\[=\log_{4} (x^2-(x^2-28))\]

Answer 6

\[=\log_{4}28\]

Answer 7

the expression is= ln4(x-sqrt(x^2-28))+ln4(x+sqrt(x^2-28))
=ln4[{x-sqrt(x^2-28)}{x+sqrt(x^2-28)}]
=ln4[x^2-(x^2-28)] using (a+b)(a-b)=a^2-b^2
=ln4[28]
=ln4[(4)(7)]
=ln4[4]+ln4[7]
=1+ln4[7]
this is simplified.

Answer 8

thank you thank you thank you so much for helping me out!