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disa [49]
4 years ago
10

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

Mathematics
1 answer:
sdas [7]4 years ago
5 0

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}

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