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Q.If x + log 10 (1 + 2 x ) = xlog 10 5 + log 10 6 then x is equal to

Q.If x + log10(1 + 2x) = xlog10 5 + log10 6 then x is equal to

Grade:12

2 Answers

Deepanshu
39 Points
6 years ago
The answer is 1.R.h.s=log5^x+log6=Log6*5^xX=log6*5^x-log(1+2^x)X=log6*5^x/1+2^x10^x=6*5^x/1+2^x2^x+2^2x=6Then put 2^x=z and solve quadratic.Regards Deepanshu
Vedant
35 Points
5 years ago
x + log(1 + 2x) = x * log(5) + log(6)
= log(10x) + log(1 + 2x) = x * log(5) + log(6)
= log(10x + 20x) = log(5x) + log(6) (by the product and power rules of logarithms)
= log(10x + 20x) = log(5x * 6)    (by the product rule of logarithms)
Now we have 2 logarithms which are equal to each other, therefore their inner components must also be equal to each other
Therefore, we have,
10x + 20x = 5x * 6
(10x + 20x) / 5x = 6
((5x * 2x) + ( 5x * 4x)) / 5x = 6
2x + 4x = 6                                                                       …..1
Now we know that 2 + 4 = 6 OR 21 + 41 = 6
On comparing this with 1, we find that x is nothing but 1

Regards
Vedant
 

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