${}^{4}log\left(64\right)=3$

${}^{4}log\left(64\right)\approx 4.3$(using the calculator)

${}^{\frac{1}{3}}log\left(60\right)\approx 3.7$(using the calculator)

${}^{\frac{1}{3}}log\left(81\right)\approx -4$

${}^{\frac{1}{3}}log\left(\frac{1}{81}\right)=4$

${}^{0.1}log\left(\mathrm{}\right)=-6$

$6^1=6$ and $6^2=36$, so $1<{}^{6}log\left(30\right)<2$.

$3^3=27$ and $3^4=81$, so $3<{}^{3}log\left(70\right)<4$.

${\left(\frac{1}{2}\right)}^{-3}=8$ and ${\left(\frac{1}{2}\right)}^{-4}=16$, so $-4<{}^{\frac{1}{2}}log\left(10\right)<-3$.

${\left(\frac{1}{3}\right)}^4\approx 0.012$ and ${\left(\frac{1}{3}\right)}^5\approx 0.004$, so $4<{}^{\frac{1}{3}}log\left(0.01\right)<5$.

$5.026$

$-8.399$

$-3.597$

$0.306$

${10}^x=0.01$, so $x={}^{10}log\left(0.01\right)=-2$.

$2^x=60$, so $x={}^{2}log\left(60\right)\approx 5.9$.

${0.8}^t=0.5$, so $t={}^{0.8}log\left(0.5\right)\approx 3.1$.