Question

3. If log 9x + log3 x = 3/2 then x is​

Answer 1

If log9 x + log3 x = 3/2 then x is 3.

Step-by-step explanation:

The required formulas:

(i) log ₐ b = log b / log a  

(ii) log aᵇ = b log a  

Considering the given equation to be as follows and thereby solving it to find the value of x:

[log₉ x ] + [log₃ x ] = $\frac{3}{2}$

⇒ $\frac{log x}{log 9}$ + $\frac{log x}{log 3}$ = $\frac{3}{2}$ ….. [from formula (i)]

⇒ $\frac{log x}{log 3^2}$ + $\frac{log x}{log 3}$ = $\frac{3}{2}$

⇒ $\frac{log x}{2 log 3}$ + $\frac{log x}{log 3}$ = $\frac{3}{2}$ ….. [from formula (ii)]

taking $\frac{log x}{log 3}$ on the L.H.S. common

⇒ $\frac{log x}{log 3}$ [$\frac{1}{2}$ + 1] = $\frac{3}{2}$

⇒ $\frac{log x}{log 3}$ [$\frac{1+2}{2}$ = $\frac{3}{2}$

⇒ $\frac{log x}{log 3}$ [3/2] = $\frac{3}{2}$

⇒ log x = log 3

removing log from both sides

⇒ x = 3

Hope this is helpful!!!