Question

Solve the equation for x:log (2x+1)×(3x-1)=0

Answer 1

Answer:

2x(3x-1)+1(3x-1)=0

6x

Answer 2

The values of x are

$x=-\frac{2}{3},\frac{1}{2}$

Step-by-step explanation:

The given equation is

$\log\:\left(\left(2x+1\right)\left(3x-1\right)\right)=0$

Using the property: $\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c$

$\left(2x+1\right)\left(3x-1\right)=10^0\\\\\left(2x+1\right)\left(3x-1\right)=1$

On expanding the expression of left hand side

$6x^2+x-1=1\\\\6x^2+x-2=0$

Solve the equation by middle term splitting method

$6x^2+4x-3x-2=0\\\\2x(3x+2)-1(3x+2)=0\\\\3x+2=0,2x-1=0\\\\x=-\frac{2}{3},\frac{1}{2}$

The values of x are

$x=-\frac{2}{3},\frac{1}{2}$

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