45=6e12.77t

Rewrite the equation as 6e12.77t=45.

6e12.77t=45

Divide each term in 6e12.77t=45 by 6.

6e12.77t6=456

Cancel the common factor of 6.

Cancel the common factor.

6e12.77t6=456

Divide e12.77t by 1.

e12.77t=456

e12.77t=456

Cancel the common factor of 45 and 6.

Factor 3 out of 45.

e12.77t=3(15)6

Cancel the common factors.

Factor 3 out of 6.

e12.77t=3⋅153⋅2

Cancel the common factor.

e12.77t=3⋅153⋅2

Rewrite the expression.

e12.77t=152

e12.77t=152

e12.77t=152

e12.77t=152

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

ln(e12.77t)=ln(152)

Expand ln(e12.77t) by moving 12.77t outside the logarithm.

12.77tln(e)=ln(152)

The natural logarithm of e is 1.

12.77t⋅1=ln(152)

Multiply 12.77 by 1.

12.77t=ln(152)

12.77t=ln(152)

Divide each term in 12.77t=ln(152) by 12.77.

12.77t12.77=ln(152)12.77

Cancel the common factor of 12.77.

t=ln(152)12.77

Simplify ln(152)12.77.

Divide 15 by 2.

t=ln(7.5)12.77

Rewrite.

t=2.0149030212.77

Divide 2.01490302 by 12.77.

t=0.1577841

t=0.1577841

t=0.1577841

Solve for t 45=6e^(12.77t)