n=12.340.04+58t

Rewrite the equation as 12.340.04+58t=n.

12.340.04+58t=n

Multiply each term by 0.04+58t and simplify.

Multiply each term in 12.340.04+58t=n by 0.04+58t.

12.340.04+58t⋅(0.04+58t)=n⋅(0.04+58t)

Cancel the common factor of 10.04+58t.

12.34=n⋅(0.04+58t)

Simplify n⋅(0.04+58t).

Apply the distributive property.

12.34=n⋅0.04+n⋅58t

Move 0.04 to the left of n.

12.34=0.04n+n⋅58t

12.34=0.04n+n⋅58t

12.34=0.04n+n⋅58t

Rewrite the equation as 0.04n+n⋅58t=12.34.

0.04n+n⋅58t=12.34

Subtract 0.04n from both sides of the equation.

n⋅58t=12.34-0.04n

Divide each term by n and simplify.

Divide each term in n⋅58t=12.34-0.04n by n.

n⋅58tn=12.34n+-0.04nn

Cancel the common factor of n.

Cancel the common factor.

n⋅58tn=12.34n+-0.04nn

Divide 58t by 1.

58t=12.34n+-0.04nn

58t=12.34n+-0.04nn

Cancel the common factor of n.

Cancel the common factor.

58t=12.34n+-0.04nn

Divide -0.04 by 1.

58t=12.34n-0.04

58t=12.34n-0.04

58t=12.34n-0.04

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

ln(58t)=ln(12.34n-0.04)

Expand ln(58t) by moving t outside the logarithm.

tln(58)=ln(12.34n-0.04)

Divide each term by ln(58) and simplify.

Divide each term in tln(58)=ln(12.34n-0.04) by ln(58).

tln(58)ln(58)=ln(12.34n-0.04)ln(58)

Cancel the common factor of ln(58).

Cancel the common factor.

tln(58)ln(58)=ln(12.34n-0.04)ln(58)

Divide t by 1.

t=ln(12.34n-0.04)ln(58)

t=ln(12.34n-0.04)ln(58)

t=ln(12.34n-0.04)ln(58)

t=ln(12.34n-0.04)ln(58)

Solve for t n=12.34/(0.04+58^t)