Question

if log9X+log3X=3/2 then find x​

Answer 1

Answer:

1.0822

Step-by-step explanation:

log9X+log3X=3/2

log9 +logx +log3+logx=3/2

log9*3+logx*x=3/2

log27+logx^2=3/2

log27*x^2=3/2

taking antilog

27*x^2= 10^3/2

x^2= (10/9)^3/2

x=  (10/9)^3/4= 1.0822

Answer 2

Answer:

The value of x is 3.      

Step-by-step explanation:

Given : Expression $\log_9 x+\log_3 x=\frac{3}{2}$

To find : The value of x?

Solution :

Expression $\log_9 x+\log_3 x=\frac{3}{2}$

$\log_(3^2) x+\log_3 x=\frac{3}{2}$

Apply logarithmic property, $\log_{a^m} b=\frac{1}{m}\log_a b$

$\frac{1}{2}\log_(3) x+\log_3 x=\frac{3}{2}$

$\log_(3) x(\frac{1}{2}+1)=\frac{3}{2}$

$\frac{3}{2}\log_(3) x=\frac{3}{2}$

$\log_(3) x=\frac{3\times 2}{2\times 3}$

$\log_(3) x=1$

Apply logarithmic property, $\log_b y=x\Rightarrow b^x=y$

$x=3^1$

$x=3$

Therefore, the value of x is 3.