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

The answer to log_{2}(3x+2)-log_{4}(x)=3 is x=(2(13+4sqrt(10)))/9 ,x=(2(13-4sqrt(10)))/9

Solve for x: log_{2}(3x+2)-log_{4}(x)=3

The solution is x=(2(13+4sqrt(10)))/9 ,x=(2(13-4sqrt(10)))/9

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

x = \frac{2 ( 13 + 4 10 )}{9}, x = \frac{2 ( 13 - 4 10 )}{9}

Decimal Notation

x = 5.69980 \dots, x = 0.07797 \dots

Solution steps

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

Apply log rules

(3 x + 2)^{2} = 64 x

Solve

(3 x + 2)^{2} = 64 x : x = \frac{2 ( 13 + 4 10 )}{9}, x = \frac{2 ( 13 - 4 10 )}{9}

x = \frac{2 ( 13 + 4 10 )}{9}, x = \frac{2 ( 13 - 4 10 )}{9}

Verify Solutions:

x = \frac{2 ( 13 + 4 10 )}{9}

True

, x = \frac{2 ( 13 - 4 10 )}{9}

True

The solutions are

x = \frac{2 ( 13 + 4 10 )}{9}, x = \frac{2 ( 13 - 4 10 )}{9}

lo g_{b} (4) = \frac{2}{3}

ln (x) + ln (x - 2) = ln (35)

ln (a) = 2

lo g_{5} (lo g_{3} (x)) = 0

lo g_{5} (x) + lo g_{x} (25) = 3

What is the answer to log_{2}(3x+2)-log_{4}(x)=3 ?
The answer to log_{2}(3x+2)-log_{4}(x)=3 is x=(2(13+4sqrt(10)))/9 ,x=(2(13-4sqrt(10)))/9
Solve for x: log_{2}(3x+2)-log_{4}(x)=3
The solution is x=(2(13+4sqrt(10)))/9 ,x=(2(13-4sqrt(10)))/9