$\"\"$

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The equation is $\"\"$ .

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Apply product property logarithm: $\"\"$ .

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$\"\"$

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$\"\"$ (Apply exponential formula: $\"\"$ )

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$\"\"$

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$\"\"$ (Evaluate power: $\"\"$ ) $\"\"$

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Subtract 100 from each side.

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$\"\"$

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$\"\"$

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Factors the left side: $\"\"$ .

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$\"\"$

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Apply zero product property: ab = 0 then a = 0 or b = 0.

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$\"\"$ $\"\"$

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Solve the first factor: $\"\"$ .

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$\"\"$ (Add 4 to each side)

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$\"\"$

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Solve the second factor: $\"\"$ .

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$\"\"$ (Add 25 to each side)

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$\"\"$

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$\"\"$

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CHECK:-

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The equation is $\"\"$ , on substitute $\"\"$ .

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$\"\"$

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Apply product property logarithm: $\"\"$ .

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$\"\"$

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$\"\"$ (Apply exponential formula: $\"\"$ )

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$\"\"$

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$\"\"$

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The solution is true. $\"\"$

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The solution is $\"\"$ .