Question

solve for x if
$log_{3}(x) + log_{9}( {x}^{2} ) + log_{27}( {x}^{3} ) = 0$
​

Answer 1

Answer:

$\huge{\boxed{\sf{X=3}}}$✔✔

Step-by-step explanation:

$\huge{\boxed{\sf{SOLUTION-}}}$

$\bold\:log_{3}(x) + log_{9}( {x}^{2} ) + log_{27}( {x}^{3} ) = 3 \\ USING\:FORMULA\:\\ = ) \frac{ log(x) }{ log(3) } + \frac{2 log(x) }{2 log(3) } + \frac{3 log(x) }{3 log(3) } = 3 \\ TALKING\:LCM\:WE\:GET\\ = ) \frac{3 log(x) }{ log(3) } = 3 \\ = ) log(x) = log(3) \\ = )x = 3$

Answer 2

Solution :-

Some properties of log

log(a) + log(b) = log(a × b)

logₐb = c → b = aᶜ

$log_{a^m}(b) = \dfrac{1}{m} log_a(b)$

$log_{a}(b^m) = m \times log_a(b)$

As told by the asker of this question Correct Question is :-

$log_{3}(x) + log_{9}( {x}^{2} ) + log_{27}( {x}^{3} ) = 3$

Now by making the Base same

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

$\rightarrow log_{3}(x) + \dfrac{2}{2}log_{3}( {x}) + \dfrac{3}{3}log_{3}({x}) = 3$

$\rightarrow log_{3}(x) + log_{3}(x) + log_{3}(x) = 3$

$\rightarrow log_3(x \times x \times x ) = 3$

$\rightarrow log_3(x^{3}) = 3$

$\rightarrow 3 \times log_3(x) = 3$

$\rightarrow log_3(x) = 1$

$\rightarrow x = 3^1$

$\rightarrow x = 3$