Indices - Solving an Equation problem

[Xeno]

Hello there, could someone help me with the following problem and show me the working out so i can apply it to other questions?

625^1-x=5

x=?

Answer must be a fraction, and to use improper fractions when necessary.

Thanks

 

[stapel]

...show me the working out so i can apply it to other questions?

You already have loads of example which "show the working"; they're in your textbook and in your class notes. So if those are leaving you lost, then one more example likely won't fix the problem. So let's try working through this one instead.

625^1-x=5

As formatted, the equation is as follows:

. . . . .\(\displaystyle 625^1\, -\, x\, =\, 5\)

However, I suspect that you omitted the grouping symbols around the "1 - x", and that the equation is actually meant to be this:

. . . . .\(\displaystyle 625^{1\, -\, x}\, =\, 5\)

The general process for solving exponential equations, when (as in this case) the base is helpful, is to convert to the same base and then equate powers. (For even more worked examples, try here.) So, think to yourself: Is 625 a power of 5? If so, what power is that? Use this to convert the left-hand side to a power of 5. Then: Is 5 a power of 5? If so, what power is that? Since this is an equation, the two sides' powers must be the same. So equate and solve.

 

[Deleted member 4993]

Hint: 625 = 5⁴