Question

log x base root3=4 then x=

Answer 1

Hey
log x
$log_{ \sqrt{3} }(x) = 4 \\ x = \sqrt{3} ^{4} \\ x =( ( \sqrt{3} ) ^{2} ) ^{2} \\ x = {3}^{2} \\ x = 9$
Answer.

Hope it helps #))

Answer 2

Answer:

Required value of x is

${3}^{ \frac{1}{8} }$

Step-by-step explanation:

Given,

$log_{x}( \sqrt{3} ) = 4$

We know,

$log_{a}(b) = c \\ b = {a}^{c}$

So,

$log_{x}( \sqrt{3} ) = 4 \\ {x}^{4} = \sqrt{3} \\ x = {( \sqrt{3}) }^{ \frac{1}{4} } \\ x = {3}^{ { \frac{1}{2} }^{ \frac{1}{4} } } \\ x = {3}^{ \frac{1}{2} \times \frac{1}{4} } \\ x = {3}^{ \frac{1}{8} }$ Some important Logarithm formulas,

$log_{x}(1) = 0\\log_{x}(0) = 1\\log_{x}(y) = \frac{ log(x) }{ log(y) } \\log( {x}^{y} ) = y log(x) \\log(x) + log(y) = log(xy) \\log(x) - log(y) = log( \frac{x}{y} ) \\ log_{x}(x) = 1$