If log k x - log 5 k-log x 5- k-1- k-0- then x is equal toA- kB- 1-5C- 5D- None of these

The correct options are B 1/5 C 5log_k x.log_5 k=log_x 5 ⇒ log_5 x=log_x 5 ⇒ log_x 5 =1/log_x 5 ⇒ (log_x 5)^2=1 ⇒ log_x 5= ± 1 ⇒ x^± 1=5 ⇒ x =5, 1/5. ...

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Byju's Answer

Standard IX

Mathematics

Fundamental Laws of Logarithms

If log k x . ...

Question

If $l o g_{k} x . l o g_{5} k = l o g_{x} 5, k \neq 1, k > 0$ , then x is equal to

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\frac{1}{5}

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None of these

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Solution

The correct options are
B $\frac{1}{5}$
C 5
$l o g_{k} x . l o g_{5} k = l o g_{x} 5 \Rightarrow l o g_{5} x = l o g_{x} 5$
$\Rightarrow l o g_{x} 5 = \frac{1}{l o g_{x} 5} \Rightarrow (l o g_{x} 5)^{2} = 1 \Rightarrow l o g_{x} 5 = \pm 1$
$\Rightarrow x^{\pm 1} = 5 \Rightarrow x = 5, \frac{1}{5} .$

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If logk x.log5 k=logx 5, k≠1, k>0, then x is equal to

The correct options are B 15 C 5logk x.log5 k=logx 5⇒log5 x=logx 5 ⇒logx 5=1logx 5⇒(logx 5)2=1⇒logx 5=±1 ⇒x±1=5⇒x=5,15.

If $l o g_{k} x . l o g_{5} k = l o g_{x} 5, k \neq 1, k > 0$ , then x is equal to