Question

logxbasek.logkbase5 = 3 ,then x=

Answer 1

Step-by-step explanation:

logx/logk. logk/log5=3

logx/log5=3

logx base5=3

X=5^3=125

Make my answer as brainlist please

Answer 2

Solution:

Given That:

$\rm \longrightarrow log_{k}(x) \times log_{5}(k) = 3$

$\rm \longrightarrow log_{k}(x) \times \dfrac{1}{ log_{k}(5) } = 3$

$\rm \longrightarrow \dfrac{ log_{k}(x)}{ log_{k}(5) } = 3$

$\rm \longrightarrow log_{5}(x) = 3$

$\rm \longrightarrow x = {5}^{3}$

$\rm \longrightarrow x = 125$

★ Therefore, the value of x satisfying the given equation is 125.

Answer:

• The value of x is 125.

Basic Concepts Required:

$\rm1. \: \: log_{a}(b) = \dfrac{1}{ log_{b}(a) }$

$\rm2. \: \: \dfrac{ log_{a}(x) }{ log_{a}(y) } = log_{y}(x)$

$\rm3. \: \: log_{a}(x) = y \: or \: x = {a}^{y}$

More To Know:

$\rm 1. \: \: log_{a}(1) = 0, \: a \neq0,1$

$\rm 2. \: \: log_{a}(a) = 1, \: a \neq0,1$

$\rm 3. \: \: log_{a}(x) = log_{a}(y) \implies x = y$

$\rm 4. \: \: log_{e}(x) = ln(x)$

$\rm5. \: \: log_{a}(x) + log_{a}(y) = log_{a}(xy)$

$\rm6.\: \: log_{a}(x) - log_{a}(y) = log_{a} \bigg( \dfrac{x}{y} \bigg)$

$\rm 7.\: \: log_{a}( {x}^{n} ) = n\log_{a}(x)$