Evaluate the following logarithmic expression
log(85)
Evaluate log(85)
You didn't enter a base
We'll do bases e and 2-10
Evaluate loge(85) 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 = 85, we have:
| loge(85) = | Ln(85) |
| Ln(e) |
Ln(e) = 1
loge(85) = 4.4426512564903
Evaluate log2(85) 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 = 85, we have:
| log2(85) = | Ln(85) |
| Ln(2) |
log2(85) = 6.4093909361377
Evaluate log3(85) 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 = 85, we have:
| log3(85) = | Ln(85) |
| Ln(3) |
log3(85) = 4.0438754438805
Evaluate log4(85) 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 = 85, we have:
| log4(85) = | Ln(85) |
| Ln(4) |
log4(85) = 3.2046954680689
Evaluate log5(85) 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 = 85, we have:
| log5(85) = | Ln(85) |
| Ln(5) |
log5(85) = 2.7603744277226
Evaluate log6(85) 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 = 85, we have:
| log6(85) = | Ln(85) |
| Ln(6) |
log6(85) = 2.4794908763085
Evaluate log7(85) 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 = 85, we have:
| log7(85) = | Ln(85) |
| Ln(7) |
log7(85) = 2.2830711164373
Evaluate log8(85) 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 = 85, we have:
| log8(85) = | Ln(85) |
| Ln(8) |
log8(85) = 2.1364636453792
Evaluate log9(85) 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 = 85, we have:
| log9(85) = | Ln(85) |
| Ln(9) |
log9(85) = 2.0219377219402
Evaluate log10(85) 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 = 85, we have:
| log10(85) = | Ln(85) |
| Ln(10) |
log10(85) = 1.9294189257143
Final Answer
log2(85) = 6.4093909361377
log3(85) = 4.0438754438805
log4(85) = 3.2046954680689
log5(85) = 2.7603744277226
log6(85) = 2.4794908763085
log7(85) = 2.2830711164373
log8(85) = 2.1364636453792
log9(85) = 2.0219377219402
log10(85) = 1.9294189257143
