A Nice Maths Problem

Ajouté : 2026-05-25

[00:00:00]Hello. You're welcome to solve this math problem, which is 4 ^ x + 4 ^ x over 2 ^ x is equal to 12.

[00:00:12]To find the value of x from this equation.

[00:00:15]Now, solution.

[00:00:17]Into here, in the numerator, 4 ^ x is common. So, we will take 4 ^ x outside the bracket. Then, 4 ^ x divided by 4 ^ x, it is 1. Plus 4 ^ x divided by 4 ^ x is 1. Bracket.

[00:00:33]Then, over this here, which is 2 ^ x, is equal to 12.

[00:00:41]Then, the next step here, it will be 4 ^ x * 1 + 1, it is 2. Then, over 2 ^ x. So, here, let's put here here, over 2 ^ x. Then, is equal to 12.

[00:00:58]Then, into here, we will divide by 2 in both sides. Also, into this side, we divide by 2.

[00:01:05]So, this and this will cancel. Then, it will be 4 ^ x over 2 ^ x is equal to 12 divided by 2, it is 6.

[00:01:18]Then, into here, power of x is common.

[00:01:21]So, it will be 4 over 2. So, here, 4 over 2. Then, bracket, this power of x, which is common, is equal to 6.

[00:01:33]Then, 4 divided by 2, it is 2 power of x is equal to 6.

[00:01:40]Then, here, we will apply log in both sides. So, it will be log of 2 ^ x is equal to log of 6.

[00:01:50]Then, this power of x will move to the base. So, it will be x e log of 2 is equal to log of six.

[00:02:01]Then here we will divide by log of two in both sides.

[00:02:07]So, this and this will cancel. Then it will be x is equal to log of six over log of two.

[00:02:18]Then into here it can be simplified more. So, it will be x is equal to log of six. Six is same as two times three.

[00:02:28]Then bracket over log of two.

[00:02:33]So, here it will be x is equal to log of two times three.

[00:02:38]It is log of two plus log of three. Then over log of two.

[00:02:49]So, here it will be x is equal to we divide by log of two in this part and this part. So, it will be this over this.

[00:02:56]So, log of two over log of two plus this over this.

[00:03:04]log of three over log of log of three over log of two.

[00:03:17]Then into here it will be x is equal to log of two divided by log of two. It is one. So, one plus log of three over log of two is same as log of three base of two.

[00:03:30]So, this is the final answer for the value of x from this our problem.

[00:03:37]Now, in the next step, let's check this answer if it is correct.

[00:03:41]So, to check from our problem which is four power of x plus four power of x over two power of x is equal to 12.

[00:03:53]Now, into here 4 ^ x + 4 ^ x there two, so it will be 2 * 4 ^ x over 2 ^ x is equal to 12.

[00:04:06]Now, into here let's substitute our our our answers into the powers of x.

[00:04:11]So, it will be 2 * 4 ^ x here we substitute here, so 1 + log of 3 base of 2.

[00:04:21]So, here power it will be 1 + log of 3 base of 2.

[00:04:28]Then over 2 ^ x to be power of 1 + log of 3 base of 2.

[00:04:37]Is it equal to 12?

[00:04:41]Then into here it will be 2 * 4 ^ 1 is same as 4 * 4 ^ of log of 3 base of 2. So, here 4 power of log of 3 base of 2.

[00:04:57]Then over here it will be 2 ^ 1 is same as 2 * 2 ^ of log of 3 base of 2. So, here power of log of 3 base of 2. Is it equal to this 12?

[00:05:13]Then from here it will be 2 * 4 it is 8.

[00:05:20]Then * here 4 4 is same as 2 squared.

[00:05:25]Then * this here log of 3 base of 2.

[00:05:31]Then over 2 * 2 ^ of log of 3 base of 2. Is it equal to 12?

[00:05:44]Now, into here it will be 8 * here 2 this two here will move to the power.

[00:05:51]So, log of 3 squared base of two then over two times two log of 3 base of two is it equal to 12.

[00:06:07]Then into here it will be 8 times two power of log of 3 squared it is 9 base of two then over two times two log of 3 base of two is it equal to 12.

[00:06:30]Now, from this part here two power of log of 9 base of two and here two power of log of 3 base of two is in the form of a power of log of b base of a which is equal to b.

[00:06:46]So, here it will be 8 times two power of log of 9 base of two is same as 9 over two times two power of log of 3 base of two is same as three then is it equal to 12.

[00:07:05]Now, here to simplify this here 8 divided by two it is four.

[00:07:12]9 divided by three it is three.

[00:07:15]Then from four times three it is 12 is equal to 12.

[00:07:21]So, left side and right side are equal.

[00:07:24]Then it is true for the value of x c is this here 1 + log of 3 base of two.

[00:07:34]Thank you for watching.

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[00:07:44]Bye-bye.