# What is the value of .8^(2/5) when using logs?

• John O' Meara
In summary, the conversation discusses the use of logarithms to find the values of .8^(2/5) and .8^(-2/5). The process involves converting .8 to 8x10^-1 and using log tables or a calculator to determine the logarithm of .8, which can then be used to find the desired value. It is also mentioned that the calculator provided by Windows can directly calculate the values without the need for logarithms.
John O' Meara
I wish to find the value of .8^(2/5) using logs. I can find the value of .8^(-2/5) as follows: =(log(8)X1/10)X-2/5
=(-1 + .9031)X-2/5 = (-.0969)X-2/5 = +.03876;
antilog(.03876) = 1.093;
Now to find .8^(2/5) my approach is the same:
log(.8)X2/5 = (log(8)X10^-1)X2/5
= (bar1 + .9031)X2/5 : what do I do next. (bar1 = -1)

It is hard to understand what you have done.

$$\log( .8^ \frac 2 5 )$$

$$= \frac 2 5 \log (.8)$$
$$= \frac 2 5 ( \log (8) - \log (10))$$

Excell tells me the answer should be ~.915

Last edited:
John O'Meara's work looks exactly like what I used to do in high school. (Of course, we did all calculations on an abacus back then!). Since a table of logarithms only gave logarithms for numbers between 1 and 10, write .8 as 8 x 10-1. Then log(.8)= log(8)- 1! It's hard to imagine anyone today doing it that way- a calculator will give immediately that log(.8)= -0.096910013008056414358783315826521, far more accurate than any table would be. 2/5 times that is
-0.038764005203222565743513326330608. (I got that, by the way, from the calculator supplied with Windows.)

Integral, log(.8) is negative. The value you give can't possibly be right.

Clarifcation:
My Excell value is for $.8 ^ \frac 2 5$ not the log.

Ah! Okay.

John O'Meara, after you have (-1+ .9031)X2/5 the obvious "next thing to do" is the multiplication: -2/5+ .36124= -.4+ .361234= -1+ .6+ .361234= -1+ .961234. Now look that up in the "body" of whatever log tables you are using: find the x that gives that logarithm. More simply you can use the calculator that comes with Windows to find the 'inverse' log of that: the inverse log of .961234 is 9.146056 so we have 9.146056x 10-1= 0.9146056. Actually, it is not at all difficult to use the Windows calculator to do .8.4 directly and see that that is, in fact, the correct answer.

## What is a logarithm?

A logarithm is the inverse function of exponentiation. It is used to solve equations and perform calculations involving exponential numbers.

## Why do we use logarithms in calculations?

Logarithms are used to simplify calculations involving large numbers or repeated multiplication. They also help in solving complex equations and analyzing data.

## How do we convert between different bases of logarithms?

To convert from one base to another, we use the change of base formula: logb(x) = loga(x) / loga(b). This allows us to convert any logarithm to a different base.

## What are some common properties of logarithms?

Some common properties of logarithms include the product property, quotient property, power property, and change of base property. These properties help in simplifying and solving logarithmic expressions.

## How do we use logarithms to solve exponential equations?

To solve exponential equations, we use the property that states logb(xy) = y * logb(x). By taking the logarithm of both sides of the equation, we can isolate the variable and solve for its value.

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