Question

If log105 + log10(5x + 1) = log10(x + 5) + 1, then x is equal to: (1)

Answer 1

Actually we're given,

$\log_{10}(5)+\log_{10}(5x+1)=\log_{10}(x+5)+1$

Since,

$\log_{m}(a)+\log_{m}(b)=\log_{m}(ab),$

We have,

$\log_{10}(5(5x+1))=\log_{10}(x+5)+\log_{10}(10)\\\\\\\log_{10}(25x+5)=\log_{10}(10x+50)$

Now,

$25x+5=10x+50\\\\\\15x=45\\\\\\\mathbf{x=3}$

Answer 2

Answer:

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