Logarithmic Equation

CAT 1997 Slot 1 · QA · Easy · Algebra

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If log⁡2[log⁡7(x2−x+37)]=1\log_2 [\log_7 (x^2 - x + 37)] = 1, then what could be the value of 'xx'?

  1. A.

    3

  2. B.

    5

  3. C.

    4

  4. D.

    None of these

Answer

C

Explanation

Given: log⁡2[log⁡7(x2−x+37)]=1\log_2 [\log_7 (x^2 - x + 37)] = 1

Taking base 2 on both sides: log⁡7(x2−x+37)=21=2\log_7 (x^2 - x + 37) = 2^1 = 2

Taking base 7 on both sides: x2−x+37=72=49x^2 - x + 37 = 7^2 = 49 x2−x−12=0x^2 - x - 12 = 0 (x−4)(x+3)=0(x - 4)(x + 3) = 0

So x=4x = 4 or x=−3x = -3. Among the given options, x=4x = 4 is option C.

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