Soms kun je van een logaritme zelf (zonder rekenmachine) de uitkomst bedenken:

• ${}^{2}log\left(16\right)$ is de oplossing van $2^t=16=2^4$.
  Dus ${}^{2}log\left(16\right)=4$.

• ${}^{3}log\left(\frac{1}{9}\right)$ is de oplossing van $3^t=\frac{1}{9}=3^{-2}$.
  Dus ${}^{3}log\left(\frac{1}{9}\right)=-2$.

• ${}^{10}log\left(10000\right)=4$ want ${10}^4=10000$.

• ${}^{10}log\left(\mathrm{0,001}\right)=-3$ want ${10}^{-3}=\mathrm{0,001}$.

• ${}^{3}log\left(\frac{1}{9}\sqrt{3}\right)=-1\frac{1}{2}$ want $3^{-1\frac{1}{2}}=\frac{1}{9}\sqrt{3}$.

• ${}^{\frac{1}{2}}log\left(8\right)=-3$ want ${\frac{1}{2}}^{-3}=8$.