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Given that 74 0.45 = x, 74 0.12 = y and x z = y 2 , then the value of z is close to:
52
0.53
99
45
0.53
To solve 74тБ░.45 = x and 74тБ░.12 = y with the relation xс╢╗ = y┬▓, we substitute the values to get (74тБ░.45)^z = (74тБ░.12)2. Equating the exponents gives 0.45z = 0.24, which simplifies to z = 0.24 / 0.45 = 24 / 45 = 8 / 15, resulting in approximately 0.533.
To solve 74тБ░.45 = x and 74тБ░.12 = y with the relation xс╢╗ = y┬▓, we substitute the values to get (74тБ░.45)^z = (74тБ░.12)2. Equating the exponents gives 0.45z = 0.24, which simplifies to z = 0.24 / 0.45 = 24 / 45 = 8 / 15, resulting in approximately 0.533.
Laws of Exponents (Indices) in Mathematics form the foundation for Quantitative Aptitude, a mandatory section in competitive exams like SSC CGL, CHSL, and UPSC CSAT.
Exponent rule: (aс╡Р)n=a(mтИЧn) is essential for simplifying power equations.
The value 0.533 is the decimal representation of the fraction 8/15.
Precision in solving exponential equations requires careful alignment of base values before equating indices.
Standardizing bases is the primary step in solving exponential equality problems in aptitude tests.
Option B (0.53) represents the calculated decimal value rounded to two places.
Options A, C, and D are incorrect as they do not satisfy the mathematical equality established by the power rule (0.45 * z = 0.24).
B is correct тАФ The value of z is derived as 8/15, which is approximately 0.53.
Mastering indices and logarithms is crucial not only for pure math sections but also for interpreting growth rate trends in Economics and Data Interpretation (DI) modules.
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