Question

Evaluate:  \(a^{25log_{a}x}-b^{25log_{b}x} = ?\)
1. 2x²⁵
2. 25x
3. 0
4. x²⁵

Answer 1

Correct Answer - Option 3 : 0

Concept:

• \(\rm {log_{a}x^b}={blog_{a}x}\)
• \(\rm a^{log_{a}x}=x\)

Calculation:

Here, we have to find the value of \(a^{25log_{a}x}-b^{25log_{b}x}\)

⇒ \(a^{25log_{a}x}-b^{25log_{b}x} = a^{log_{a}x^{25}}-b^{log_{b}x^{25}}\)       ( ∴ \(\rm {log_{a}x^b}={blog_{a}x}\))

= x²⁵ - x²⁵ = 0         ( ∴ \(\rm a^{log_{a}x}=x\))

Hence, option C is correct.