Question

Find the value of x if \(4^{log_{2}4}+4^{log_{16}4}=5^{log_{x}18}\)
1. 25
2. 5
3. 1
4. e

Answer 1

Correct Answer - Option 2 : 5

Concept:

• \(a^{log_{b}a}=\sqrt{a}\), If b = a², a > 0, b > 0, b \( \neq\) 1
• \(a^{log_{b}a}=a^2\), If a = b2, a > 0, b > 0, b \( \neq\) 1

Calculation:

Given: \(4^{log_{2}4}+4^{log_{16}4}=5^{log_{x}18}\)

⇒ \(4^2+\sqrt4=5^{log_{x}18}\)

⇒ \(16+2=5^{log_{x}18}\)

⇒ \(18=5^{log_{x}18}\)

Take log on both side to base 5 we get

⇒ \({log_{5}18}={log_{x}18} \times {log_{5}5}\)

⇒ \({log_{5}18}={log_{x}18}\)

By comparing both LHS and RHS, we get

⇒ x = 5

Hence, option B is correct.