What is the solution to 2log9 (x) = log^9 (8) + log9 (x-2)

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Mathematics

Lucia Travis

14 July, 18:54

What is the solution to 2log9 (x) = log^9 (8) + log9 (x-2)

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Olivia Duke · Answer 1

2log9 (x) = log^9 (8) + log9 (x-2)

Log₉x² = log₉8 + log₉ (x-2)

Log₉x² = log₉ (8 * (x-2))

Log₉x² = log₉8x-16

Log₉x² - log₉8x-16 = 0

Log₉ (x² / (8x-16)) = 0

x² / (8x-16) = 9°

x² = 1 * 8x-16

x²-8x+16 = 0

x²-4x-4x+16 = 0

x (x-4) - 4 (x-4) = 0

(x-4) (x-4) = 0

Therefore x = 4 ...