Solve for x: (i) log105+log105x+1=log10 x+5+1 - Maths - Indices and Logarithms

Question

Solve for x: (i) log 10 5 + log 10 5 x + 1 = log 10  
x + 5 + 1

Abhishek Jha · Accepted Answer

Dear student,
Here is the solution of your asked query:
log105+log105x+1=log10x+5+1     ⇒log105×5x+1-log10x+5=1            {since, loga+logb=loga×b}⇒log105×5x+1x+5=1                                 {Since, loga-logb=logab}⇒log105×5x+1x+5=log1010⇒5×5x+1x+5=10⇒25x+5=10x+50⇒15x=45⇒x=4515=3
Regards

Solve for x: (i) log 10 5 + log 10 5 x + 1 = log 10 x + 5 + 1

Solve for x: (i) $\log_{10} 5 + \log_{10} (5 x + 1) = \log_{10} (x + 5) + 1$