How do you solve #2^ { 7x + 2} = 5^ { x }#?

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Answer 1 · 2017-07-21T10:52:57

#- frac(2 ln(2))(7 ln(2) - ln(5))#

We have: #2^(7 x + 2) = 5^(x)#

Let's apply #ln# to both sides of the equation:

#Rightarrow ln(2^(7 x + 2)) = ln(5^(x))#

Using the laws of logarithms:

#Rightarrow (7 x + 2) ln(2) = x ln(5)#

#Rightarrow 7 x ln(2) + 2 ln(2) = x ln(5)#

#Rightarrow 7 x ln(2) - x ln(5) = - 2 ln(2)#

#Rightarrow x (7 ln(2) - ln(5)) = - 2 ln(2)#

#therefore x = - frac(2 ln(2))(7 ln(2) - ln(5))#