Question

If log5 + log(5x+1) = log(x+5) + 1, then x is equal to

Answer 1

Answer:

$log5 + log(5x + 1) = log(x + 5) + 1 \\ \therefore \: log5 + log(5x + 1) = log(x + 5) + log10 \\ ..( \because \: log10 = 1)\\ \therefore \: log \{5 \times (5x + 1) \} = log \{(x + 5) \times 10 \} \\ \implies \: 5(5x + 1) = 10(x + 5) \\ \implies5x + 1 = 2(x + 5) \\ \implies \: 5x + 1 = 2x + 10 \\ \implies \: 5x - 2x = 10 - 1\\ \implies \: 3x = 9\\ \implies \: x = \frac{9}{3} \\ \implies \: \huge \fbox{x = 3}$

Answer 2

The value of x is 3.

Step-by-step explanation:

Since we have given that

$\log5+\log(5x+1)=\log(x+5)+1$

As we know that

$\log 10=1\\\\and\ \log m+\log n=\log mn$

So, it becomes,

$\log 5+\log (5x+1)=\log (x+5)+\log 10\\\\\log 5(5x+1)=\log 10(x+5)\\\\5(5x+1)=10(x+5)\\\\25x+5=10x+50\\\\25x-10x=50-5\\\\15x=45\\\\x=\dfrac{45}{15}\\\\x=3$

Hence, the value of x is 3.

# learn more:

Log5+log(5x+1)=log(x+5)+1​

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