A Nice Exponential Problem

Added: 2026-05-15

[00:00:00]Hello. How to solve this math problem which is 4^ x / 10 is = 8 to find the value of x from this equation.

[00:00:13]Now solution from our problem which is 4^ x / 10 is = 8 is same as 8 / 1 into here we will cross multiply then here it will be 4^ x * 1 it is 4^ x is equal to 10 * 8 it is 8.

[00:00:48]Then into here we will apply log in both sides. So it will be log of this 4^ x is equal to log of 8.

[00:01:02]Then this power of x will move to the base. So it will be x * log of 4 is = log of 8.

[00:01:14]Then into here I'll divide by log of four on both sides. So it will be over log of four and into this side over log of 4. So this log of four cancel as log of four. Then it will be x is equal to log of 80 over log of four.

[00:01:38]Then in the next step it will be x is = to log of 80 to 4 80 is same as 4 * 20 then bracket over log of 4. Then into here it will be x is equal to log of 4 * 20 is same as log of 4. Then plus log of 20 then over this log of 4. Then into here it will be x is equal to weide by log of four in here and here. So it will be log of 4 over log of 4 plus log of 20 over log of 4. Then here it will be x = log of 4 / log of 4 it is 1 plus log of 20 over log of 4.

[00:02:49]Then into here will be x is = 1 + log of 20 to 4. 20 is same as 4 * 5. Then bracket over log of 4.

[00:03:06]Then into here it will be x is = 1 + log of 4 * 5 is same as log of 4 then plus log of 5 then over log of 4. So into here it will be x is = 1 + weide by log of four in here and here. So it will be this over this. So it will be log of 4 over log of 4 + log of 5 / log of 4.

[00:03:44]So here it will be x is = 1 + log of 4 / log of 4 is 1. So 1 + log of 5 over log of 4. So into here will be x is = 1 + 1 it is 2 + log of 5 over log of 4. 4 is same as 2².

[00:04:12]So into here will be x = 2 + will be log of 5 / this square will move to the base. So it will be 2 log of 2.

[00:04:26]So here will be x = 2 + a same as 1 / 2.

[00:04:32]So 1 / 2 log of 5 / log of 2 is same as log of 5 base of two. So this is the final answer for the value of x into this our problem.

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[00:05:10]Bye-bye.