Because 32 = 25, that's how. So 1/32 = 1/(25) = 2-5.priceofcarrot said:There isn't a problem here, it's an example they gave, but I don't get how you can get the answer without using logs.
2^(2x+1) = 1/32
2^(2x+1) = 2^(-5)
How do they know that it's -5?
You know that 32 = 9, right, so 33 = 27. That's all it is.priceofcarrot said:Same thing for:
3^(x-1) = 27
3^(x-1) = 3^3
No, it's not trial and error. It's useful to know a few powers of small numbers.priceofcarrot said:Is it just trial and error? I've tried a bunch of different methods but none have worked.
Just memorize some of the powers, as Mark44 said. It really isn't much different than memorizing addition and multiplication facts (except that the numbers are bigger, of course).priceofcarrot said:Is there any simple formula I can use to find that 32 = 2^5? Or similar things, or is it just having an idea which numbers as the exponent would produce which numbers?
Can I just knowing 32 = 2^x find out what x is with a formula?
priceofcarrot said:Is there any simple formula I can use to find that 32 = 2^5? Or similar things, or is it just having an idea which numbers as the exponent would produce which numbers?
Can I just knowing 32 = 2^x find out what x is with a formula?
An exponent is a number that represents how many times a base number is multiplied by itself. It is written as a superscript to the right of the base number, such as 23 where 2 is the base and 3 is the exponent.
Logs are used to find the exponent when the base and the result are known. However, if the base and the result are not known, logs cannot be used to find the exponent. In this case, alternative methods such as trial and error or using a calculator with an exponent function can be used.
Trial and error is a method of finding the exponent by repeatedly guessing different values until the correct one is found. This method can be time-consuming and may not always result in an accurate answer, but it can be useful when other methods are not available.
Yes, most scientific calculators have an exponent function that can be used to find the exponent. This function is usually denoted by the symbol "^" or "xy". By inputting the base and the result, the calculator can provide the correct exponent value.
Apart from trial and error and using a calculator, there are other mathematical techniques that can be used to find the exponent, such as the Newton-Raphson method or the bisection method. However, these methods may require a more advanced understanding of mathematics and are not commonly used for finding exponents.