Solve -3*e^(2m-5)-7=-34

Evaluate

- 3 e^{2 m - 5} - 7 = - 34

Move the expression to the left side

- 3 e^{2 m - 5} - 7 - (- 34) = 0

Subtract the numbers

More Steps

- 3 e^{2 m - 5} + 27 = 0

Rewrite the expression

- 3 e^{2 m - 5} = - 27

Change the sign

3 e^{2 m - 5} = 27

Divide both sides

\frac{3 e ^{2 m - 5}}{3} = \frac{27}{3}

Divide the numbers

e^{2 m - 5} = \frac{27}{3}

Divide the numbers

More Steps

e^{2 m - 5} = 9

Take the logarithm of both sides

ln (e^{2 m - 5}) = ln (9)

Evaluate the logarithm

2 m - 5 = ln (9)

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

2 m = ln (9) + 5

Divide both sides

\frac{2 m}{2} = \frac{ln ( 9 ) + 5}{2}

Divide the numbers

m = \frac{ln ( 9 ) + 5}{2}

Solution

More Steps

m = \frac{2 ln ( 3 ) + 5}{2}

Alternative Form

m \approx 3.598612

Solve the equation