SOLUTION: please solve the logarithmic equation. log(5)^(1/5)=(x/8) so far i have.....(1/5)=5^(x/8)

Question 608198: please solve the logarithmic equation.
log(5)^(1/5)=(x/8)
so far i have.....(1/5)=5^(x/8)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First, you should not be using the exponent indicator. "^", in your expression. Nothing in your equation is being raised to some power.

Admittedly expressing logarithms using a keyboard is difficult. To make your problem clear (and clearly expressed problems are more likely to draw the help of a tutor), please use more English. For example
base 5 log of 1/5 = x/8
or
log, base 5, of 1/5 = x/8
Or, you could could teach yourself algebra.com's formula syntax. Click on "View source" to see what I typed to get:

Although is correct and although we often rewrite logarithmic equations in exponential form like you have, gets us no closer to a solution. In fact, since the variable is now "buried" in an exponent, we are actually farther away from the solution!?

The logarithmic equations which we do rewrite in exponential form have the variable in the argument (or base) of a logarithm. This is not true for your equation. The variable in your equation is already "out in the open". It is not buried inside a logarithm.

Whenever you are solving any equation, logarithmic or otherwise, stay focused on your goal. At the end you want an equation in the form:
x = ....
or
.... = x
In other words, we want the variable all by itself on one side of the equation.

To get your variable all by itself we just have to get rid of that 8. Multiplying both sides of the equation by 8 we get:

All that is left is to simplify the left side, if possible. If you really get what logarithms are, you will understand how to simply your logarithm. In general, logarithms are exponents. Your specific logarithm, , represents "the exponent you would put on a 5 to get 1/5". So what power of 5 equals 1/5? If you understand your exponents well, you know that the answer is: -1 (since ). So your logarithm simplifies to -1. Now we have:

which simplifies to:
-8 = x
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