If x-1 log 10 x 2-log 10 x 2-x-13- then the value-s of x is-areA- 1000B- 2C- 0-1D- 100

The correct options are A 1000 B 2 C 0.1We have, nbsp;x 1log10x2 log10x2=x 13, nbsp;x gt;0, nbsp;x≠1⇒x 1=1 nbsp;or nbsp;log10x2 log10x2=3⇒x=2 nbsp ...

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Byju's Answer

Standard XII

Mathematics

Fundamental Laws of Logarithms

If x-1 log 10...

Question

If ${(x - 1 |}_{10}^{{({log}_{10} x)}^{2} - {log}_{10} x^{2}} = {(x - 1 |}^{3}$ , then the value/s of x is/are

1000

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0.1

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100

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Solution

The correct options are
A 1000
B 2
C 0.1
We have, ${(x - 1 |}_{10}^{{({log}_{10} x)}^{2} - {log}_{10} x^{2}} = {(x - 1 |}^{3}, x > 0, x \neq 1 \Rightarrow (x - 1 | = 1 or {({log}_{10} x)}^{2} - {log}_{10} x^{2} = 3 \Rightarrow x = 2 or {({log}_{10} x)}^{2} - 2 {log}_{10} x - 3 = 0 \Rightarrow x = 2 or (({log}_{10} x - 3) ({log}_{10} x + 1)] = 0 \Rightarrow x = 2 or {log}_{10} x = 3, {log}_{10} x = - 1 \Rightarrow x = 2, x = 10^{3} = 1000, x = 10^{- 1} = 0.1$

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If (x−1|(log10x)2−log10x2=(x−1|3 , then the value/s of x is/are

The correct options are A 1000 B 2 C 0.1We have, (x−1|(log10x)2−log10x2=(x−1|3, x>0, x≠1⇒(x−1|=1 or (log10x)2−log10x2=3⇒x=2 or (log10x)2−2log10x−3=0⇒x=2 or ( (log10x−3) (log10x + 1)]=0⇒x=2 or log10x=3, log10x=−1⇒x=2, x=103=1000, x=10−1=0.1

If ${(x - 1 |}_{10}^{{({log}_{10} x)}^{2} - {log}_{10} x^{2}} = {(x - 1 |}^{3}$ , then the value/s of x is/are