What is the answer to 4tln(t)=ln(t) ?

The answer to 4tln(t)=ln(t) is t=1,t= 1/4

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4tln(t)=ln(t)

4 t ln (t) = ln (t)

t = 1, t = \frac{1}{4}

Decimal Notation

t = 1, t = 0.25

Solution steps

4 t ln (t) = ln (t)

Move

ln (t)

to the left side

4 t ln (t) - ln (t) = 0

Factor

4 t ln (t) - ln (t) : ln (t) (4 t - 1)

ln (t) (4 t - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

ln (t) = 0 or 4 t - 1 = 0

Solve

ln (t) = 0 : t = 1

Solve

4 t - 1 = 0 : t = \frac{1}{4}

Verify Solutions:

t = 1

True

, t = \frac{1}{4}

True

The solutions are

t = 1, t = \frac{1}{4}

lo g_{3} (x + 4) + lo g_{3} (x + 1) = 2

1.5 = - lo g_{10} (T)

lo g_{10} (x) = 8.935, x

lo g_{2} (x + 1) = lo g_{3} (2 7^{2})

lo g_{x} (42) = 10