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[tex]\boxed{\boxed{\pink{\bf \leadsto The \ Solution \ of \ the \ given \ equation \ is\ \sqrt{26}\ or \ -\sqrt{26}}}}[/tex]
We need to find the solution of the given logarithmic equation. So the given equation is ,
[tex]\bf \implies ln ( x^2-25) = 0 [/tex]
Using the Properties of log we can write this as ,
[tex]\bf \implies e^{ln(x^2-25)} = e^0 \:\:\bigg\lgroup \red{\bf Here \ e \ is \ Euler's \ Number }\bigg\rgroup \\\\\bf\implies x^2-25 = e^0 \\\\\bf\implies x^2-25 = 1 \\\\\bf\implies x^2=25+1\\\\\bf\implies x^2=26 \\\\\bf\implies x = \sqrt{26} \\\\\bf\implies\boxed{\red{\bf x = \sqrt{26},-\sqrt{26}}}[/tex]