What is the answer to 1+2log_{4}(t+1)=2log_{2}(t) ?

The answer to 1+2log_{4}(t+1)=2log_{2}(t) is t=1+sqrt(3)

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1+2log_{4}(t+1)=2log_{2}(t)

1 + 2 lo g_{4} (t + 1) = 2 lo g_{2} (t)

t = 1 + 3

Decimal Notation

t = 2.73205 \dots

Solution steps

1 + 2 lo g_{4} (t + 1) = 2 lo g_{2} (t)

Apply log rules

4 (t + 1)^{2} = t^{4}

Solve

4 (t + 1)^{2} = t^{4} : t = 1 + 3, t = 1 - 3

t = 1 + 3, t = 1 - 3

Verify Solutions:

t = 1 + 3

True

, t = 1 - 3

False

The solution is

t = 1 + 3

lo g_{5} (3 x - 2) = 1 + lo g_{5} (x - 4)

ln (x + 5) = 2

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

20 = 20 lo g_{10} (x)

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

What is the answer to 1+2log_{4}(t+1)=2log_{2}(t) ?
The answer to 1+2log_{4}(t+1)=2log_{2}(t) is t=1+sqrt(3)
Solve for t: 1+2log_{4}(t+1)=2log_{2}(t)
The solution is t=1+sqrt(3)