CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms
If log₂x + log₄x = 6, then the value of x is:
Convert log to base 2 using log base 4 of x equals half of log base 2 of x. The equation becomes one and a half times log base 2 of x equals 6, so log base 2 of x is 4. Hence x equals 2 to the power 4, which is 16.
- A8
- B16Correct
- C32
- D64
Explanation
Use change of base: log₄x = (1/2)log₂x. The equation becomes (3/2)log₂x = 6, so log₂x = 4 and x = 2⁴ = 16. The option 64 results from wrongly taking log₂x = 6 and ignoring the second term.
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