Question

What is the solution to log Subscript 2 Baseline (9 x) minus log Subscript 2 Baseline 3 = 3 x = three-eighths x = eight-thirds x = 3 x = 9

Answer 1

Option B: $x=\frac{8}{3}$ is the solution

Explanation:

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

We need to determine the solution for the given expression.

The solution can be determined by solving the expression for x.

Adding $\log _{2} 3$ to both sides of the expression, we have,

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

Using the logarithmic definition that if $\log _{a}(b)=c$ then $b=a^{c}$

Thus, we have,

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

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

Simplifying, using the identity $a^{\log _{a}(b)}=b$, we have,

$9 x=8\cdot 3$

Multiplying, we get,

$9x=24$

Dividing both sides by 9, we have,

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

Simplifying, we have,

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

Thus, the solution of the expression is $x=\frac{8}{3}$

Answer 2

Answer:

x=8/3

Step-by-step explanation: