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

n=12.340.04+58t
Rewrite the equation as 12.340.04+58t=n.
12.340.04+58t=n
Solve for t.
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)