Solve 3(2^(2t-5))-4=10

Evaluate

3 \times 2^{2 t - 5} - 4 = 10

Move the expression to the left side

3 \times 2^{2 t - 5} - 4 - 10 = 0

Subtract the numbers

3 \times 2^{2 t - 5} - 14 = 0

Rewrite the expression

3 \times 2^{2 t - 5} = 14

Divide both sides

\frac{3 \times 2 ^{2 t - 5}}{3} = \frac{14}{3}

Divide the numbers

2^{2 t - 5} = \frac{14}{3}

Take the logarithm of both sides

lo g_{2} (2^{2 t - 5}) = lo g_{2} (\frac{14}{3})

Evaluate the logarithm

2 t - 5 = lo g_{2} (\frac{14}{3})

Move the constant to the right-hand side and change its sign

2 t = lo g_{2} (\frac{14}{3}) + 5

Divide both sides

\frac{2 t}{2} = \frac{lo g _{2} ( \frac{14}{3} ) + 5}{2}

Divide the numbers

t = \frac{lo g _{2} ( \frac{14}{3} ) + 5}{2}

Solution

More Steps

t = \frac{6 + lo g _{2} ( 7 ) - lo g _{2} ( 3 )}{2}

Alternative Form

t \approx 3.611196

Solve the equation