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**+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

CPhill
Mar 28, 2018