Question

What is the solution to log Subscript 2 Baseline (9 x) minus log Subscript 2 Baseline 3 = 3

Answer 1

The value of x is  $\frac{8}{3}$

 Explanation:

The expression is  $\log _{2}(9 x)-\log _{2}(3)=3$  

Adding  $\log _{2}(3)$ to both sides of the equation,  we get,

$\log _{2}(9 x)=3+\log _{2}(3)$

Using log definition, if  $\log _{a}(b)=c$  then  $b=a^{c}$ , we have,

 $9 x=2^{3+\log _{2}(3)}$

Using exponent rule, $a^{b+c}=a^{b} a^{c}$,

$9x=2^{\log _{2}(3)} \cdot 2^{3}$

Simplifying, we have,

$9x=3\cdot8\\9x=24$

Dividing both sides by 9, we have,

$x=\frac{24}{9}$

Simplifying,

$x=\frac{8}{3}$

Thus, the value of x is $\frac{8}{3}$