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Luden [163]
3 years ago
10

Please helllppp . . . only give answer if you are 100% sure it's correct please!!

Mathematics
1 answer:
SOVA2 [1]3 years ago
4 0

Condene the logarithms on the left side by applying the property, ln(<em>a</em>) - ln(<em>b</em>) = ln(<em>a</em> / <em>b</em>):

ln(<em>x</em> - 2) - ln(<em>x</em> - 3) = 1

→   ln((<em>x</em> - 2) / (<em>x</em> - 3)) = 1

Now take the exponential of both sides:

exp(ln((<em>x</em> - 2) / (<em>x</em> - 3))) = exp(1)

(<em>x</em> - 2) / (<em>x</em> - 3) = <em>e</em>

Solve for <em>x</em> :

<em>x</em> - 2 = <em>e</em> (<em>x</em> - 3)

<em>x</em> - 2 = <em>e x</em> - 3<em>e</em>

<em>x</em> - <em>e x</em> = 2 - 3<em>e</em>

(1 - <em>e</em>) <em>x</em> = 2 - 3<em>e</em>

<em>x</em> = (2 - 3<em>e</em>) / (1 - <em>e</em>) ≈ 3.582

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