Solving for x in logs with different bases

Question

Hi, Im trying to solve for x for Ln(x)—log(x)=1 

 

The first thing I did was use change of base property. After this is where Im totally confused on solving. 

Answer 1

hello Kyle,

As you mentioned you can use of base property:

log(x)=ln(x)/ln(10)

substituting this in your equation now you have:

ln(x)-(ln(x)/ln(10)) = 1

the easiest way to solve this, for me, is to get rid of the denominator by multiplying both sides of the equation by ln(10)

==>  ln(10)ln(x)-ln(x) = ln(10)

==> (ln(10)-1)ln(x) = ln(10) either by taking a common factor or just subtraction.

==> ln(x) = ln(10)/(ln(10)-1)

==> x = e^{ln(10)/(ln(10)-1)}

==> x ≈2.851803603 by using a calculator

Hope that helps!

Bader A.