Question

Please give an accurate answer and show work.

Answer 1

Answer:

3.06

Step-by-step explanation:

$\log_{5}(\dfrac{2}{3}x-2)+2=0\\\\\log_{5}(\dfrac{2}{3}x-2)=-2$

This means that 5 to the power of -2 is $(\dfrac{2}{3}x-2)$, meaning that:

$\dfrac{2}{3}x-2=5^{-2}=\dfrac{1}{25} \\\\\dfrac{2}{3}x=\dfrac{51}{25} \\\\2x=\dfrac{153}{25} \\\\x=\dfrac{153}{50}=3.06$

Hope this helps!