Evaluate the following logarithmic expression
logof200
Evaluate logof200
You didn't enter a base
We'll do bases e and 2-10
Evaluate loge(200) 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 = 200, we have:
| loge(200) = | Ln(200) |
| Ln(e) |
Ln(e) = 1
loge(200) = 5.298317366548
Evaluate log2(200) 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 = 200, we have:
| log2(200) = | Ln(200) |
| Ln(2) |
log2(200) = 7.6438561897747
Evaluate log3(200) 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 = 200, we have:
| log3(200) = | Ln(200) |
| Ln(3) |
log3(200) = 4.8227363021502
Evaluate log4(200) 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 = 200, we have:
| log4(200) = | Ln(200) |
| Ln(4) |
log4(200) = 3.8219280948874
Evaluate log5(200) 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 = 200, we have:
| log5(200) = | Ln(200) |
| Ln(5) |
log5(200) = 3.2920296742202
Evaluate log6(200) 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 = 200, we have:
| log6(200) = | Ln(200) |
| Ln(6) |
log6(200) = 2.9570472251115
Evaluate log7(200) 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 = 200, we have:
| log7(200) = | Ln(200) |
| Ln(7) |
log7(200) = 2.7227965120179
Evaluate log8(200) 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 = 200, we have:
| log8(200) = | Ln(200) |
| Ln(8) |
log8(200) = 2.5479520632582
Evaluate log9(200) 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 = 200, we have:
| log9(200) = | Ln(200) |
| Ln(9) |
log9(200) = 2.4113681510751
Evaluate log10(200) 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 = 200, we have:
| log10(200) = | Ln(200) |
| Ln(10) |
log10(200) = 2.301029995664
Final Answer
log2(200) = 7.6438561897747
log3(200) = 4.8227363021502
log4(200) = 3.8219280948874
log5(200) = 3.2920296742202
log6(200) = 2.9570472251115
log7(200) = 2.7227965120179
log8(200) = 2.5479520632582
log9(200) = 2.4113681510751
log10(200) = 2.301029995664
