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aisha
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Find the exact value of x: 25^x-30(5^x)+125=0 what is the common base? I thought it was 5 but not for 30.
Nope. Observe that 2*3^4 = 2*(3^4) = 2*3*3*3*3. On the other hand, (2*3)^4 = 2*2*2*2*3*3*3*3 which is definitely not equivalent.aisha said:First of all can the -30(5^x) be multiplied? to =-150^x
Note that your equation can be written (5^x)^2 - 30(5^x) + 125 = 0, so if A = 5^x, the equation becomes A^2 - 30A + 125 = 0.aisha said:Next I let A=5^x and then my equation became A^2-30+125=0 so A^2+95 I don't think I did this right and if I did then what do I do next A=square root of -95?
hypermorphism said:Nope. Observe that 2*3^4 = 2*(3^4) = 2*3*3*3*3. On the other hand, (2*3)^4 = 2*2*2*2*3*3*3*3 which is definitely not equivalent.
Note that your equation can be written (5^x)^2 - 30(5^x) + 125 = 0, so if A = 5^x, the equation becomes A^2 - 30A + 125 = 0.
Plug the values of x you solved for back into the original equation to see if they work.aisha said:Ok I factored that and got (A-5) (A-25) A=5 or A=25 sooo 5^x=5 or 5^x=25
x=1 or x=2 are my solutions correct? Can there be two values for x?
Yeah! This is the best method to vertify the answer.Plug the values of x you solved for back into the original equation to see if they work.
The equation 25^x-30(5^x)+125=0 is a common base equation that represents a mathematical relationship between two variables, x and y. It is used to solve for the value of x when the equation is set to equal 0.
The value of x is determined by using algebraic techniques to solve for the variable. This usually involves isolating the variable on one side of the equation and simplifying the other side. The resulting value of x will make the equation true.
The common base, which is 5 in this equation, is important because it allows for the use of logarithms to solve for the value of x. Logarithms are useful in solving exponential equations with different bases by converting them into a common base equation.
Yes, there are restrictions on the value of x in this equation. If the exponent of the common base (5) is negative, the equation will result in a complex solution. Therefore, the value of x must be a positive real number in order for the equation to have a real solution.
This equation can be used in various fields such as finance, physics, and chemistry to determine the value of x in different scenarios. For example, it can be used to calculate the growth rate of investments, the decay rate of radioactive materials, or the concentration of a substance in a chemical reaction.