How do you solve 3.14159^x=43.14159x=4?

1 Answer
Jul 21, 2016

x=ln(4)/ln(3.14159)=log_3.14159(4)x=ln(4)ln(3.14159)=log3.14159(4)

Explanation:

We will use the property of logarithms that ln(a^x) = xln(a)ln(ax)=xln(a)

With that:

3.14159^x = 43.14159x=4

=> ln(3.14159^x)=ln(4)ln(3.14159x)=ln(4)

=> xln(3.14159)=ln(4)xln(3.14159)=ln(4)

:. x=ln(4)/ln(3.14159)

Note that this is eqivalent to the base 3.14159 log of 4, a result we could have also found by taking the base 3.14159 log of both sides and applying log_a(a^x)=x