Solving Logarithms Examples

Example 1

${\log }_4(2x+6)=3$ $4^3=2x+6$ $64=2x+6$ $58=2x$ $x=29$

Example 2

$\log {(}^3\sqrt{x^2+48x})=\frac{2}{3}$ $10^{2/3}{=}^3\sqrt{x^2+48x}$ $10^2=x^2+48x$ $x^2+48x-100=0$ $(x+50)(x-2)=0$ $x=-50Ux=2$ check if these values of x result in the argument being positive

Interval Method

x(x+48) > 0 Critical values are 0 and -48

Test	x < -48	-48 < x < 0	0 < x
x(x+48)	+	-	+

-50 is OK 2 = OK