Question

Please Hurry! What is the solution to log2_(9x)-log2_3=3?

Answer 1

Answer:

$\log _2\left(9x\right)-\log _2\left(3\right)=3 : x = \frac{8}{3}$

Decimal:

$x = 2.66666...$

Step-by-step explanation:

$\log _2\left(9x\right)-\log _2\left(3\right)=3$

Add $log _2\left(3)$ to both sides:

$\log _2\left(9x\right)-\log _2\left(3\right)+\log _2\left(3\right)=3+\log _2\left(3\right)$

Simplify:

$\log _2\left(9x\right)=3+\log _2\left(3\right)$

Use the logarithmic definition: If $\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c$

$\log _2\left(9x\right)=3+\log _2\left(3\right)\quad \Rightarrow \quad \:9x=2^{3+\log _2\left(3\right)}$

$9x=2^{3+\log _2\left(3\right)}$

Expand $2^{3+\log _2\left(3\right)} : 24$

$9x=24$

Solve: $9x=24 : x = \frac{8}{3}$

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

Verify solutions: $x = \frac{8}{3}$  : True

The solution is:

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

Hope I helped. If so, may I get brainliest and a thanks?

Thank you, have a good day! =)

Answer 2

Answer:

$log_{2}(9x) - log_{2}(3) = 3 \\ 3 = log_{2}(8) or log_{2}( {2}^{3} ) \\ log_{2}( \frac{9x}{3} ) = log_{2}(8) \\ \frac{9x}{3} = 8 \\ 9x = 8 \times 3 \\ 9x = 24 \\ x = \frac{24}{9} \\ x = \frac{8}{3} \\ x = 2 \times \frac{2}{3}$