You can use same operations on both sides such that both sides' x value come on one side and rest of the values go on other side so that you get what is equal to x.
The value of x is 6
How does [tex]a^b = a^c[/tex] implies = c ?
It is because [tex]a^x[/tex] where x is a variable and "a" is a constant, is a function. A function only outputs single value to each input.
If for x = p and x = q, we get same value, then we will have [tex]a^x[/tex] not being a function. Thus, for that to be a function, we need those inputs same too for output to be same.
Thus, [tex]a^p = a^q \implies p = q[/tex]
Remember that we need base to be same(here a is base and p and q are exponents)
How to solve the given equation?
We can use the fact that 64 is cube of 3 and can use the above stated fact.
Thus, we have:
[tex]4^{(x+30)} = 64^{(2x)}\\4^{x+30} = 4^{3^{2x}} \\\\\text{since power of power will multiply, thus,}\\\\4^{x + 30} = 4^{6x}\\\\or\\\\x+30 = 6x\\\\\text{Subtracting x on both sides}\\\\30 = 5x\\\\\text{Dividing by 5 on both sides}\\\\6 = x\\x = 6[/tex]
Thus, The value of x is 6
Learn more about base and exponent here:
https://brainly.com/question/15722035
