Question

If 5=a^x, then 5/a=?​

Answer 1

Answer:

Step-by-step explanation:

To find the expression for 5/a, you first need to solve the equation 5=a^x for a.  To solve for a, raise both sides of the equation to the 1/x power.  

5=a^x

5^(1/x)=(a^x)^(1/x)              (now multipy exponents)

5^(1/x)=a                           (x*1/x = 1 - the exponent on a)

Now that the equation is solved for a, substitute the left side of the equation into 5/a.  So,

5/a = 5/5^(1/x)             (since the bases are the same, 5, subtract the exponents; note that the exponent in the numerator = 1)

5/a = 5^(1 - 1/x)           (subtract by getting lcd, x)

5/a = 5^((x-1)/x)

Just to show you that this works:  Let a = 25 and x = 1/2.

We know that 5 = a^x = 25^(1/2) = sqrt(25)=5.

Now, 5/a should equal 5/25 = 1/5, so let's plug the numbers into the new expression.

5/a = 5^((.5-1)/.5)   (I'm using .5 instead of 1/2 so it's not so many parentheses.)