What is the answer to log_{x}(8x-3)-log_{x}(4)=2 ?

The answer to log_{x}(8x-3)-log_{x}(4)=2 is x= 3/2 ,x= 1/2

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log_{x}(8x-3)-log_{x}(4)=2

lo g_{x} (8 x - 3) - lo g_{x} (4) = 2

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

Decimal Notation

x = 1.5, x = 0.5

Solution steps

lo g_{x} (8 x - 3) - lo g_{x} (4) = 2

Add

lo g_{x} (4)

to both sides

lo g_{x} (8 x - 3) - lo g_{x} (4) + lo g_{x} (4) = 2 + lo g_{x} (4)

Simplify

lo g_{x} (8 x - 3) = 2 + lo g_{x} (4)

Apply log rules

8 x - 3 = x^{2} \cdot 4

Solve

8 x - 3 = x^{2} \cdot 4 : x = \frac{3}{2}, x = \frac{1}{2}

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

Verify Solutions:

x = \frac{3}{2}

True

, x = \frac{1}{2}

True

The solutions are

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

2 lo g_{8} (x + 2) = lo g_{8} (2 x + 19)

lo g_{5} (x + 5) - lo g_{5} (x - 3) = 1

lo g_{10} (6 x) - 3 = - 4

ln (x + 3) = ln (x) + ln (3)

0 = ln (2 x + 3)

What is the answer to log_{x}(8x-3)-log_{x}(4)=2 ?
The answer to log_{x}(8x-3)-log_{x}(4)=2 is x= 3/2 ,x= 1/2
Solve for x: log_{x}(8x-3)-log_{x}(4)=2
The solution is x= 3/2 ,x= 1/2