Question

log3 x +log9 x +log27 x =11/2

Answer 1

hope it helps you........

Answer 2

Answer:

The solution of the expression is x=27.

Step-by-step explanation:

Given : Expression $\log_3 x+\log_9 x+\log_{27}x=\frac{11}{2}$

To find : Solve the expression ?

Solution :

$\log_3 x+\log_9 x+\log_{27}x=\frac{11}{2}$

$\log_3 x+\log_{3^2} x+\log_{3^3}x=\frac{11}{2}$

Using logarithmic property, $\log_{b^m}a=\frac{1}{m}\log_b a$

$\log_3 x+\frac{1}{2}\log_{3} x+\frac{1}{3}\log_{3}x=\frac{11}{2}$

$\log_3 x(1+\frac{1}{2}+\frac{1}{3})=\frac{11}{2}$

$\frac{11}{6}\log_3 x=\frac{11}{2}$

$\log_3 x=\frac{11\times 6}{2\times 11}$

$\log_3 x=3$

Using logarithmic property, $\log_b a=c\Rightarrow a=b^c$

$x=3^3$

$x=27$

Therefore, The solution of the expression is x=27.