If (log)kxlog˙5k=(log)x5,k=1,k>0, then x is equal to k (b) 1/5 (c) 5 (d) none of these

Solution: logyx=logcylogcx(logklogx)⋅(log5logk)=logxlog5(logx)2=(log5)2logx=log5x=5.

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If $(lo g)_{k} x \dot{lo g}_{5} k = (lo g)_{x} 5, k \neq = 1, k > 0,$ then $x$ is equal to $k$ (b) 1/5 (c) 5 (d) none of these

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(lo g)_{k} x \dot{lo g}_{5} k = (lo g)_{x} 5, k \neq = 1, k > 0,

then

x

is equal to

k

(b) 1/5 (c) 5 (d) none of these

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Solution:

lo g_{y}^{x} = \frac{lo g _{c}^{x}}{lo g _{c}^{y}}

(\frac{lo g x}{lo g k}) \cdot (\frac{lo g k}{lo g 5}) = \frac{lo g 5}{lo g x}

(lo g x)^{2} = (lo g 5)^{2}

lo g x = lo g 5

x = 5

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Question Text	If $(lo g)_{k} x \dot{lo g}_{5} k = (lo g)_{x} 5, k \neq = 1, k > 0,$ then $x$ is equal to $k$ (b) 1/5 (c) 5 (d) none of these
Answer Type	Text solution:1
Upvotes	150