## Enter natural log statement

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

loge(85) = 4.4426512564903
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

loge(85) = 4.4426512564903
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
##### How does the Logarithms and Natural Logarithms and Eulers Constant (e) Calculator work?
Free Logarithms and Natural Logarithms and Eulers Constant (e) Calculator - This calculator does the following:
* Takes the Natural Log base e of a number x Ln(x) → logex
* Raises e to a power of y, ey
* Performs the change of base rule on logb(x)
* Solves equations in the form bcx = d where b, c, and d are constants and x is any variable a-z
* Solves equations in the form cedx=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z
* Exponential form to logarithmic form for expressions such as 53 = 125 to logarithmic form
* Logarithmic form to exponential form for expressions such as Log5125 = 3

This calculator has 1 input.

### What 8 formulas are used for the Logarithms and Natural Logarithms and Eulers Constant (e) Calculator?

Ln(a/b) = Ln(a) - Ln(b)
Ln(ab)= Ln(a) + Ln(b)
Ln(e) = 1
Ln(1) = 0
Ln(xy) = y * ln(x)

For more math formulas, check out our Formula Dossier

### What 4 concepts are covered in the Logarithms and Natural Logarithms and Eulers Constant (e) Calculator?

euler
Famous mathematician who developed Euler's constant
logarithm
the exponent or power to which a base must be raised to yield a given number
natural logarithm
its logarithm to the base of the mathematical constant e
eLn(x) = x
power
how many times to use the number in a multiplication