- #1
amd123
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Homework Statement
simplify m^(9*√5)/m^(√5)
The Attempt at a Solution
would that equal m^9 or m^(8*√5)
amd123 said:and thanks for your help with the first one :) really appreciate it
amd123 said:right now I am stuck on this problem (1/6)^x = 36^(x+3) if i solve it by making the bases equal to 36 by multiplying 1/6 by -2 i get -2x but then for x i get -3 which obviously would not work, but if i use -2 as x the equation works BUT how do i get -2 from that equation?
amd123 said:my alg2 teacher said inorder to solve (1/6)^x = 36^(x+3) you need to make the BASES equal to each other i can easily make 1/6 to 36 by raising it to -2 but then i have to multiply x by -2. How do the log identities work?
A square root is the number that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5x5=25.
To simplify square roots, you need to find the largest perfect square factor of the number inside the square root symbol. Then, you can take the square root of that factor and place it outside the symbol. The remaining number inside the symbol should have no perfect square factors. For example, √48 can be simplified to 4√3.
To add or subtract square roots, you must first make sure that the numbers inside the symbol are the same. If they are not, you can use the method of simplifying square roots to make them the same. Then, you can add or subtract the numbers outside the symbol while keeping the number inside the symbol the same. For example, √18 + 2√18 can be simplified to 3√18.
To multiply or divide square roots, you can simply multiply or divide the numbers outside the symbol and multiply or divide the numbers inside the symbol. If there are any perfect squares inside the symbol, you can simplify them using the method mentioned in question 2. For example, √12 x √3 can be simplified to 2√3.
To solve equations with square roots, you need to isolate the square root on one side of the equation and square both sides. This will eliminate the square root and allow you to solve for the variable. However, you must always check your solutions to make sure they satisfy the original equation, as squaring both sides can introduce extraneous solutions. For example, to solve √(x+2)=6, you would square both sides and solve for x, but then you must plug in your solution to make sure it works in the original equation.