If 2y = 50
then y*log(2) = log(50)
so that y = log(50)/log(2) = 5.6439 (approx).
NB: The logarithms can be taken to any base >1.
the base and the laws of exponent
An expression using a base and exponent takes the form ( a^n ), where ( a ) is the base and ( n ) is the exponent. The base represents a number that is multiplied by itself, while the exponent indicates how many times the base is used in the multiplication. For example, in the expression ( 2^3 ), 2 is the base and 3 is the exponent, meaning ( 2 \times 2 \times 2 = 8 ).
A base number is the value to the power of the exponent. For example, in 2^4, 2 is the base number and 4 is the exponent.
You answered your own question?
The exponent can only be found in the context of a base. But there is no base specified and so there can be no clear answer.On possible answer is that 262144 = 512^2 so, with the base 512, the exponent is 2.
You can define any base you like and calculate an appropriate exponent or, you can pick an exponent and calculate the base. So you can have base 25, with exponent 2 or base 5 and exonent 4 or base e (the base for natural logarithms) and exponent 6.437752 (to 6 dp) or base 10 and exponent 2.795880 (to 6 dp) or base 2 and exponent 9.287712 etc or base 8.54988 (to 3 dp) and exponent 3 or base 3.623898 (to 3 dp) and exponent 5 etc There is no need for the base to be an integer or even rational. Probably the most important bases in advanced mathematics is e, which is a transcendental number. Similarly, there is no need for the exponent to be an integer.
11
You can choose the base to be any number (other than 0, -1 and 1) and calculate the appropriate exponent, or you can choose any exponent and calculate the appropriate base. For example, base 10: 121 = 10^2.08278537 (approx) Or exponent = 10: 121 = 1.615394266^10 (approx). I expect, though, that the answer that is required is 121 = 11^2.
4 is the base, 2 is the exponent.
The two are related. The answer could be base 2, exponent 18 or base 8, exponent 6 or base 10, exponent 5.4185 or base 262144, exponent 1 or base 68,719,476,736 and exponent 0.5
the base and the laws of exponent
The base could be 11 and the exponent 2, giving 112 But, it could equally be base = 14641, and exponent = 0.5, or base = 10, and exponent = 2.082785 (approx)
A base number is the value to the power of the exponent. For example, in 2^4, 2 is the base number and 4 is the exponent.
You answered your own question?
The exponent can only be found in the context of a base. But there is no base specified and so there can be no clear answer.On possible answer is that 262144 = 512^2 so, with the base 512, the exponent is 2.
When the base is squared.
The base and its exponent are fundamental components of exponential expressions. The base is the number that is being multiplied, while the exponent indicates how many times the base is multiplied by itself. For example, in the expression (2^3), 2 is the base and 3 is the exponent, meaning 2 is multiplied by itself three times (2 × 2 × 2). This relationship highlights how exponential growth or decay occurs, with the base determining the rate of change influenced by the exponent.