Evaluate the following logarithmic expression
log1000
Evaluate log1000
You didn't enter a base
We'll do bases e and 2-10
Evaluate loge(1000) using the Change of Base Formula
The formula for the change of base rule in logb(x) is as follows:
| logb(x) = | Ln(x) |
| Ln(b) |
Given b = e and x = 1000, we have:
| loge(1000) = | Ln(1000) |
| Ln(e) |
Ln(e) = 1
loge(1000) = 6.9077552789821
Evaluate log2(1000) using the Change of Base Formula
The formula for the change of base rule in logb(x) is as follows:
| logb(x) = | Ln(x) |
| Ln(b) |
Given b = 2 and x = 1000, we have:
| log2(1000) = | Ln(1000) |
| Ln(2) |
log2(1000) = 9.9657842846621
Evaluate log3(1000) using the Change of Base Formula
The formula for the change of base rule in logb(x) is as follows:
| logb(x) = | Ln(x) |
| Ln(b) |
Given b = 3 and x = 1000, we have:
| log3(1000) = | Ln(1000) |
| Ln(3) |
log3(1000) = 6.2877098228682
Evaluate log4(1000) using the Change of Base Formula
The formula for the change of base rule in logb(x) is as follows:
| logb(x) = | Ln(x) |
| Ln(b) |
Given b = 4 and x = 1000, we have:
| log4(1000) = | Ln(1000) |
| Ln(4) |
log4(1000) = 4.982892142331
Evaluate log5(1000) using the Change of Base Formula
The formula for the change of base rule in logb(x) is as follows:
| logb(x) = | Ln(x) |
| Ln(b) |
Given b = 5 and x = 1000, we have:
| log5(1000) = | Ln(1000) |
| Ln(5) |
log5(1000) = 4.2920296742202
Evaluate log6(1000) using the Change of Base Formula
The formula for the change of base rule in logb(x) is as follows:
| logb(x) = | Ln(x) |
| Ln(b) |
Given b = 6 and x = 1000, we have:
| log6(1000) = | Ln(1000) |
| Ln(6) |
log6(1000) = 3.8552916268154
Evaluate log7(1000) using the Change of Base Formula
The formula for the change of base rule in logb(x) is as follows:
| logb(x) = | Ln(x) |
| Ln(b) |
Given b = 7 and x = 1000, we have:
| log7(1000) = | Ln(1000) |
| Ln(7) |
log7(1000) = 3.5498839873648
Evaluate log8(1000) using the Change of Base Formula
The formula for the change of base rule in logb(x) is as follows:
| logb(x) = | Ln(x) |
| Ln(b) |
Given b = 8 and x = 1000, we have:
| log8(1000) = | Ln(1000) |
| Ln(8) |
log8(1000) = 3.3219280948874
Evaluate log9(1000) using the Change of Base Formula
The formula for the change of base rule in logb(x) is as follows:
| logb(x) = | Ln(x) |
| Ln(b) |
Given b = 9 and x = 1000, we have:
| log9(1000) = | Ln(1000) |
| Ln(9) |
log9(1000) = 3.1438549114341
Evaluate log10(1000) using the Change of Base Formula
The formula for the change of base rule in logb(x) is as follows:
| logb(x) = | Ln(x) |
| Ln(b) |
Given b = 10 and x = 1000, we have:
| log10(1000) = | Ln(1000) |
| Ln(10) |
log10(1000) = 3
Final Answer
log2(1000) = 9.9657842846621
log3(1000) = 6.2877098228682
log4(1000) = 4.982892142331
log5(1000) = 4.2920296742202
log6(1000) = 3.8552916268154
log7(1000) = 3.5498839873648
log8(1000) = 3.3219280948874
log9(1000) = 3.1438549114341
log10(1000) = 3
