how to solve 1^ x + 4^ x = 16 power x find the value of x so at first we divided by 16 power x in both sides so divided by 16 power x ided by 16 power x ided 16 power x now we see uh this this will be cancel so here one here one Now 1 powerx iD 16 powerx that means it will be 1 over 16 then uh bracket common power x according to this formula a power n of B power n is equal to a of B then bracket common power n that means uh NN same power but different base here x x same power but different base then plus again x x same power but different B so according to this exponential rule we can write here for of 16 then bracket common power x is equal to 1 divided 1 that means it will be 1 now uh 1 by 16 can be written as 1X 4 bracket power 2 1 square is same as 1 over over 4 square is same as 16 then this first bracket can be written as second bracket then power of X plus uh we see uh 4id 4 ided 4 that means it will be 1 16 ided 4 that means it will be uh 4 so we have one of 4 then bracket power of X is equal to 1 now here we can apply this exponential rule that a power M bracket power n is equal to a power n bracket power n so according to this rule we can write here 1X 4 bracket power x then second bracket power of two then plus 1X 4 bracket power x is equal to one now we see m 1 by 4 braet 4X 1 by 4 braet 4X both term is same so let 1 by 4 bracket power x is substituted by T so our equation will be t² plus T then is equal to one now I can write here t² plus T then this plus one take to the left side so this will be minus one then is equal to0 now uh here you can apply quadratic formula so you can write here T is equal to Min - B plus or minus a square root of b² - 4 a / 2 a here a is As on then B is as one after that c is as minus one now we can write here t will be equal to uh minus B that means on then plus or minus a square root of b² that means it will be 1 squ minus 4 times a that means on time uh C that means uh 1 so bracket1 then divided by 2 time a that means one now I can write here T is equal to Min - one plus or minus square root of 1 square is same as 1 then minus * minus that means it will be plus then 4 * on * on that means it will be 4 then divided by 2 * on that means 2 now we can write here T is equal to uh - one plus or minus a square root of 1 + 4 that means it will be 5 then ided by 2 now we see here two cases so we can write here T is equal to - one uh - one plus Square < TK of 5 ided 2 or t is equal to minus one minus Square Ro TK of 5 divided by 2 now remember that let 1X 4 braet 4X is substituted by T So T that means 1X 4 braet power x so T that means it will be 1X 4 bracket power x is equal to plus squ otk of 5 that means Square < TK of 5 then - 1 / 2 or t that means 1 by 4 bra 4X so 1X 4 braet power x is = to - 1 minus Square < TK of 5 ided by 2 now we see 1 by 4 braet power any number is always positive but -1 - < TK 5 / 2 this is must be negative so positive cannot be equal to negative so this is rejected now uh from here I take log in both sides you can write here log log of 1x 4 bracket power x is equal to log of square < TK of 5 - 1 ided by 2 now uh here you can apply rule that log M Power R is equal to R log M that means this power are move to the Base According to this rule I can compare here this power x will move to the base you can write here x log 1 by 4 is equal to log of square < TK of 5- 1 divided by 2 now we need the value of x so we divide it by log of 1x4 in both sides so divided by log of 1x 4 ided by log of 1x 4 now we see uh this log of 1 by 4 this log of 1 by 4 will be cancel so here x will be equal to this divided by this that means it will be log of aunk of 5 - 1 over 2 then uh base of 1 by 4 so uh this is the value of x so this is our final answer how to solve x^ x^ 3 is = 36 find the value of x so we have x^ x^ 3 then is equal to 36 is same as 6^ 2 now we have X power x^ 3 is equal to 6^ 2 now uh we multiply by power of three in both sides so multiply by power of three multiply power of 3 now x^ 3 then bracket uh bracket power of X Cub according to this rule a power M bracket power n is equal to a power n bracket power M then is equal to 6 power of 2 * 3 that means it will be six now uh I can write here x^ 3 will be equal to 6 according to this rule a power a is equal to n^ n so a will be equal to n where n is greater than or equal to one now we need the value of x so we multiply by power of 1x 3 in both sides so multiply by power of 1 by 3 multiply multip by power of 1 by 3 so this three this three will be cancel so here x power one is same as X is equal to 6 power of 1 by 3 can be written as cube root of 6 so cube root of 6 this is the value of x so this is our final answer