Objective:

To perform exponentiation with the C, D and L Scales.

General:

• To perform this operation, i.e to calculate y if y=a^b, we make use of the fact that:

• Depending on the type of calculation, this method can be more accurate than using the LL scales.

Method:

• Using the L scale determine the logarithm of the base.  (Adjust the characteristic if necessary.)
• Transfer this value to the D scale.
• Multiply by the exponent.
• Subtract the characteristic (integer value) if not equal to zero.
• Transfer this value to the L scale.
• Read the result on the D scale.
• Multiply by the power of ten determined by the previous characteristic.

 

Example 1:  Determine the value of 3.2^2.4.

• Move the cursor to D3.2 (the base)
• Read the value L0.505 (no adjustment for the characteristic needed)
• Move the cursor to D0.505
• Set C10 above D0.505
• Move cursor to C2.4 (the exponent)
• Read the result D1.21
• Subtract 1 (the characteristic), giving 0.21
• Move the cursor to L0.21
• Read the result D1.62

• Multiply by 10¹ (1 from the subtracted characteristic)
• Answer: 16.2

 

Example 2:  Determine the value of 24.6^2.68.

• Move the cursor to D24.6 (the base)
• Read the value L0.391, adjust the characteristic, hence log1024.6=1.391
• Move the cursor to D1.391
• Set C1 above D1.391
• Move cursor to C2.68 (the exponent)
• Read the result D3.73
• Subtract 3 (the characteristic), giving 0.73
• Move the cursor to L0.73
• Read the result D5.36

• Multiply by 10³ (3 from the subtracted characteristic)
• Answer: 5360

 

Practice Questions:  Determine the following values.

1. 5.6^3.6 (Ans: 490)
2. 41.2^3.64 (Ans: 759000)