Question

Evaluate the following.1.Log4^1/8=?2.log100^0.001=?3.log8^0.00625=?​

Answer 1

Answer:

$\log 4^{\frac{1}{8}}=0.07525\\\\\log 100^{0.001}=0.002\\\\\log 8^{0.00625}==0.00564375$

Step-by-step explanation:

Property of Log used here: $\log m^n=n\log m,\ \log 2=0.3010299957,\ \log 10=1$

1.

$\log 4^{\frac{1}{8}}=\frac{1}{8}\log 4\ \ \ \ \ \ \ \ \ \ using\ \log m^n=m\log n\\\\\log 4^{\frac{1}{8}}=\frac{1}{8}\log 2^2\\\\\log 4^{\frac{1}{8}}=\frac{1}{8}\times 2\log 2\ \ \ \ \ \ \ \ \ \ using\ \log m^n=m\log n\\\\\log 4^{\frac{1}{8}}=\frac{1}{4}\times 0.3010\\\\\log 4^{\frac{1}{8}}=0.07525$

2.

$\log 100^{0.001}=0.001\log 100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ using\ \log m^n=n\log m\\\\\log 100^{0.001}=0.001\log 10^2\\\\\log 100^{0.001}=0.001\times 2\log 10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ using\ \log m^n=n\log m\\\\\log 100^{0.001}=0.001\times 2\ \ \ \ \ \ \ \ \ \ \ \ as\ \log 10=1\\\\\log 100^{0.001}=0.002$

3.

$\log 8^{0.00625}=0.00625\log 8\ \ \ \ \ \ \ \ \ \ using\ \log m^n=m\log n\\\\ \log 8^{0.00625}=}=0.00625\log 2^3\\\\\\log 8^{0.00625}==0.00625\times 3\log 2\ \ \ \ \ \ \ \ \ \ using\ \log m^n=m\log n\\\\\log 8^{0.00625}==0.00625\times 3\times 0.3010\\\\\log 8^{0.00625}==0.00564375$