Hello!

I encountered a equation where im having trouble finding x

The equation is \(lg(1,5x+14) + lg2 = 0,5 * lg{x}^{4}\)

First i used the first logarithm law which gave me \(lg(3x + 24) = 0,5 * lg{x}^{4}\)

Then i used the third law which gave me \(lg(3x + 24) = 0,5 * 4 *lgx\)

Then what do i do :P

Thankfull for any help <3

kilander
Sep 14, 2017

#1**+2 **

log (1.5x + 14) + log (2) = 0.5 log (x^4)

Other than a slight mistake, you were on the right track..... let's go from your last step

log (3x + 28) = 0.5 * 4 log (x)

log (3x + 28 ) = 2 * log (x)

Let's write the "2" back as an exponent

log (3x + 28) = log (x^2)

Since the we have a single log on each side....we can forget those and solve this :

3x + 28 = x^2 rearranging, we have that

x^2 - 3x - 28 =0 this is factorable as

(x -7) ( x+4) = 0

Setting both factors to 0 and solving for x, we have that x = 7 or x = -4

Note that both solutions will solve the simplified form of the problem ,i.e., log (3x + 28) = log (x^2) !!!!

CPhill
Sep 14, 2017