Answer:
[tex]x=\dfrac{8}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]\log_2(9x)-\log_23=3[/tex]
As the logs have the same base, we can apply the Quotient log law:
[tex]\log_ax - \log_ay=\log_a\left(\dfrac{x}{y}\right)[/tex]
Therefore:
[tex]\implies \log_2(9x)-\log_23=3[/tex]
[tex]\implies \log_2\left(\dfrac{9x}{3}\right)=3[/tex]
[tex]\implies \log_2(3x)=3[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 2^3=3x[/tex]
[tex]\implies 8=3x[/tex]
Divide both sides by 3:
[tex]\implies x=\dfrac{8}{3}[/tex]
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