# Find the value of x if $25^{log_{5}25}-9^{log_{81}9}=7^{log_{7}x}$

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Find the value of x if $25^{log_{5}25}-9^{log_{81}9}=7^{log_{7}x}$
5. 81

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Correct Answer - Option 2 : 622

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:  $25^{log_{5}25}-9^{log_{81}9}=7^{log_{7}x}$

By using the properties mentioned in the concept part we get

⇒ $25^2-\sqrt9=7^{log_{7}x}$

⇒ $625-3=7^{log_{7}x}$

⇒ $622=7^{log_{7}x}$

By taking log on both sides to the base 7 we get

⇒ ${log_{7}622}={log_{7}x} \times {log_{7}7}$

⇒ ${log_{7}622}={log_{7}x}$

By comparing LHS and RHS, we get x = 622

Hence, option 2 is correct.