What is the answer to log_{2x}(1-3x)=2 ?

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

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log_{2x}(1-3x)=2

lo g_{2 x} (1 - 3 x) = 2

x = \frac{1}{4}

Decimal

x = 0.25

Solution steps

lo g_{2 x} (1 - 3 x) = 2

Apply log rules

\frac{ln ( 1 - 3 x )}{ln ( 2 x )} = 2

Multiply both sides by

ln (2 x)

\frac{ln ( 1 - 3 x )}{ln ( 2 x )} ln (2 x) = 2 ln (2 x)

Simplify

ln (1 - 3 x) = 2 ln (2 x)

Apply log rules

1 - 3 x = 4 x^{2}

Solve

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

x = \frac{1}{4}, x = - 1

Verify Solutions:

x = \frac{1}{4}

True

, x = - 1

False

The solution is

x = \frac{1}{4}

2 n^{2} lo g_{2} (n) = n^{3}

20 lo g_{10} (x) = - 40

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

y, - ln (y) = ln (x)

- 3.01 = 20 lo g_{10} (K)

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