Question

Log x is the exponent to which the base 10 must be raised to get ____. So, we can complete the following table for log x.

Short answer

x	103	102	101	100	${10}^{-1}$	${10}^{-2}$	${10}^{-3}$	${10}^{1/2}$
log x	3	2	1	0	$-1$	$-2$	$-3$	$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

Step-by-step solution

Step 1. Given.

Given x-values are${10}^3,{10}^2,{10}^1,{10}^0,{10}^{-1},{10}^{-2},{10}^{-3},{10}^{1/2}.$

Step 2. To determine.

We have to find log x for the given x-values.

Step 3. Calculation.

We’ll use the formula: $\log \left({10}^k\right)=k$.

For ${10}^3,{10}^2,{10}^1,{10}^0,{10}^{-1},{10}^{-2},{10}^{-3}\mathrm{and}{10}^{1/2}$, the corresponding values ofk are $3,2,1,0,-1,-2,-3,\mathrm{and}½$.

So, the table is given by:

x	103	102	101	100	${10}^{-1}$	${10}^{-2}$	${10}^{-3}$	${10}^{1/2}$
log x	3	2	1	0	$-1$	$-2$	$-3$	$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$