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find the exact solution to the equation below

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Hi Dalia, so here it goes
                                                                            Steps
log(x3) + log(x4)/log(100x) = 5                      Multiply log(100x) on both sides                          
log(x3) + log(x4) = 5log(100x)                       logM + logN = logMN, M = x3, N = x4
log[(x3)(x4) = 5log(100x)                              Add exponents on left hand side
log(x3+4)=5log(100x)                                    rlogM = logMr
log(x7) = log(100x)5                                     Bring 100x to the 5th power using (as)t = as x t
log(x7) = log10,000x5                                   If logM = logN, then M=N, M=x7, N=10,000x5
x7 = (1x1010)x5                                           Set equation to 0 by subtracting (1x1010)x5 on both sides
x7 - (1x1010)x5 = 0                                           Take out Greatest Common Factor(GCF) of x5
x5(x2 - (1x1010)) = 0                                         Set each part equal to 0 and solve
x5 = 0                      ;      x2 - (1x1010) = 0
(x5)1/5 = (0)1/5        ;            +1x10^10      1x10^10  
x = 0                       ;       (x2)1/2=(1x1010)1/2
                                        x = ±100,000
So, x =0,100
Now Check your solution
x = 0 => log(0)3 + log(0)4/log(100(0) = 5              
              You cannot do the log0, because the there is a logarthms are undefined at x = 0 where there is  .             a vertical asymptote at y=0   
x = -100,000, logarthms cannot be negative
x=100,00 => log(100,000)3 + log(100,000)4/log(100)(100,000) = 5
                     => 15+20/7 = 5
                     =>  35/7 = 5
                     =>       5 = 5
The exact solution is x = 100,000
 
Happy to help, feel free to rate me
Shannon