If log k x -log 5 k-log x 5- k-0- k-1- then x is equal to

The correct options are B 15 C 5log_kx·log_5k=log_x5; k gt;0,k≠1 ⇒log x·log klog k·log 5=log_x5 ⇒log xlog 5=log_x5 ⇒log_5x=1log_5x nbsp; ⇒ (log_5x)^2=1 ⇒log ...

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Byju's Answer

Standard XII

Mathematics

Fundamental Laws of Logarithms

If log k x ·l...

Question

If ${log}_{k} x \cdot {log}_{5} k = {log}_{x} 5, k > 0, k \neq 1,$ then $x$ is equal to

k

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\frac{1}{5}

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Solution

The correct options are
B $\frac{1}{5}$
C $5$
${log}_{k} x \cdot {log}_{5} k = {log}_{x} 5; k > 0, k \neq 1$
$\Rightarrow \frac{log x \cdot log k}{log k \cdot log 5} = {log}_{x} 5$
$\Rightarrow \frac{log x}{log 5} = {log}_{x} 5$
$\Rightarrow {log}_{5} x = \frac{1}{{log}_{5} x}$
$\Rightarrow ({log}_{5} x)^{2} = 1$
$\Rightarrow {log}_{5} x = \pm 1$
$\Rightarrow x = \frac{1}{5}, 5$

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If logkx⋅log5k=logx5, k>0,k≠1, then x is equal to

The correct options are B 15 C 5logkx⋅log5k=logx5; k>0,k≠1 ⇒logx⋅logklogk⋅log5=logx5 ⇒logxlog5=logx5 ⇒log5x=1log5x ⇒(log5x)2=1 ⇒log5x=±1 ⇒x=15,5

If ${log}_{k} x \cdot {log}_{5} k = {log}_{x} 5, k > 0, k \neq 1,$ then $x$ is equal to