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Help Me, please

 

Solve the logarithmic equation, rounding decimal answers to the thousandths place 

 

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

 

x=

ManuelBautista2019  Mar 28, 2018
 #1
avatar+86859 
+1

log (2x)  + log (x -5)    = 2

 

We can use this rule to simplify things, Manuel

 

log a  + log b  =  log (a * b)....so ....we can write the left sides as

 

log[ (2x * (x -5) ]  = 2

 

log [  2x^2 - 10x]  =  2      in exponential form we have

 

10^2  = 2x^2 - 10x

 

100  =  2x^2  - 10x        rearrange as

 

2x^2 - 10x - 100  = 0       divide through by 2

 

x^2 - 5x -50  =  0        factor as

 

(x - 10)(x + 5)  = 0

 

Setting each factor to 0 and solve for x  and we have that

 

x  = 10     or   x  = -5

 

We must reject  x  = -5   because it would mean that we would be taking logs of negative numbers in the original equation

 

So.....x  = 10

 

 

cool cool cool

CPhill  Mar 28, 2018

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