Answer:
[tex]x = \frac{8}{3}[/tex] is the solution to [tex]\log_2 9x - \log_2 3 = 3[/tex]
Step-by-step explanation:
Using the logarithmic rules:
[tex]\log \frac{m}{n} = \log m -\log n[/tex]
if [tex]\log_b x = a[/tex] then;
[tex]x = b^a[/tex]
Given the equation:
[tex]\log_2 9x - \log_2 3 = 3[/tex]
Solve for x:
Apply the logarithmic rules:
[tex]\log_2 \frac{9x}{3} = 3[/tex]
⇒[tex]\log_2 3x = 3[/tex]
Apply the logarithmic rules;
[tex]3x = 2^3[/tex]
⇒[tex]3x = 8[/tex]
Divide both sides by 3 we have;
[tex]x = \frac{8}{3}[/tex]
Therefore, the solution for the given equations is, [tex]x = \frac{8}{3}[/tex]
