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2(5^(x+2))=5(2^(x+5)) 

 May 18, 2018
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Solve for x :

2 5^(x + 2) = 5 2^(x + 5)

 

Take the natural logarithm of both sides and use the identities log(a b) = log(a) + log(b) and log(a^b) = b log(a):

log(5) (x + 2) + log(2) = log(2) (x + 5) + log(5)

 

Expand out terms of the left hand side:

log(5) x + log(2) + 2 log(5) = log(2) (x + 5) + log(5)

 

Expand out terms of the right hand side:

log(5) x + log(2) + 2 log(5) = log(2) x + 5 log(2) + log(5)

 

Subtract x log(2) + log(2) + 2 log(5) from both sides:

(log(5) - log(2)) x = 4 log(2) - log(5)

 

Divide both sides by log(5) - log(2):

 

x = (4 log(2) - log(5))/(log(5) - log(2))=1.2694123......

 May 18, 2018

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