Solve exponential equation like a pro| secret method |

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[00:00:00]how to solve this equation on the board.

[00:00:01]Welcome to my channel. We have the cube root of 3 to the power of x is equal to 3 to the power of 1 over the root of x.

[00:00:11]All right, by the end of this video you will know the solution to this equation.

[00:00:14]So, watch this video to the end.

[00:00:16]We shall have solution.

[00:00:20]Now, the equation says the cube root of 3 to the power of x is equal to 3 to the power of 1 divided by the root of x.

[00:00:35]Now, let me show you how to transform this the cube root.

[00:00:39]If you have a or if you have the cube root of a this can be transformed as what? A to the power of 1 over 3.

[00:00:51]Law of indices.

[00:00:53]So, by using this law, let's transform this in this form.

[00:00:57]So, we shall have 3 to the power of x all to the power of what? 1 over 3 to be equal to what? 3 to the power of 1 over root of x.

[00:01:12]Now, x * 1 over 3 we shall have 3 to the power of um x over 3 to be equal to 3 to the power of 1 divided by the root of x.

[00:01:27]>> [snorts] >> Now, also if you have x to the power of m to be equal to x to the power of n, that means m is equal to n because we have the same base.

[00:01:41]Now, in here, we shall equate the powers because the base are the same, which become x over 3 to be equal to 1 divided by the root of x.

[00:01:54]So, what do you do?

[00:01:56]You cross multiply.

[00:01:58]So, if you multiply this by this, we shall have x multiplied by the root of x will be equal to 1 * 3 is 3.

[00:02:09]Now, I am looking for a way to clear this x, I mean this square root. What do I do?

[00:02:14]Let me square it both side.

[00:02:16]If I square this side, of course, I'm squaring everything here and squaring everything here.

[00:02:21]This square affect both x and root of x.

[00:02:25]So, I can rewrite this as x squared multiplied by the root of x squared to be equal to what? 3 squared is 9.

[00:02:39]Which means this will cancel out this, we shall have an x squared is multiplying x because square root has canceled out squared, which become x squared multiplied by x. Of course, this has a natural power of 1 to be equal to 9.

[00:02:56]We have x.

[00:02:57]Now, when we have the same base when multiplying the same base, we add we add the powers, which become x to the power of 2 + 1 is 3 to be equal to 9.

[00:03:10]Now, to solve this let's take the cube root of both side.

[00:03:16]The cube root of x cubed to be equal to the cube root of 9.

[00:03:24]This will cancel out this. This implies that our x will be equal to the cube root of 9.

[00:03:32]And that happens to be our solution, the cube root of 9. Thank you for watching.

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[00:03:42]Thank you.