We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
199
1
avatar+50 

2(5^(x+2))=5(2^(x+5)) 

 May 18, 2018
 #1
avatar
+1

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

7 Online Users

avatar