Question:medium

If (_2128=a), (_3813=b), then (a-2b=)

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Whenever you see a logarithm with radical signs in the base or argument, instantly convert them into fractional exponents using (\[n\]x = x^1/n). Then use the rules (_b^k(b^m) = mk) to find values directly without writing multiple steps! For example, (_2^1/2(2^7) = 71/2 = 14).
Updated On: Jun 10, 2026
  • (3)
  • (5)
  • (7)
  • (9)
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Recall what a logarithm means.
A logarithm just asks, to what power must we raise the base to get the number. We will use the power rule, that $\log_b(m^n) = n\,\log_b m$, and the rule for a power in the base, that $\log_{b^k} m = \frac{1}{k}\log_b m$.

Step 2: Simplify the first logarithm to find $a$.
Write the number and base as powers of the same value. Using the rules above, the first expression collapses to a clean whole number, giving $a = 9$.

Step 3: Simplify the second logarithm to find $b$.
Do the same for the second term. Express its number and base as powers of one common value, apply the power rules, and it reduces to $b = 2$.

Step 4: Form the required combination.
The question asks for $a - 2b$. We now have $a = 9$ and $b = 2$.

Step 5: Substitute the values.
Put the numbers in carefully. \[ a - 2b = 9 - 2\times 2 = 9 - 4 \]

Step 6: Do the final arithmetic.
Subtracting gives $9 - 4 = 5$. So the value of the expression is \[ \boxed{5} \]
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