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.
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 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)
The base is 7 and the exponent is 3.
The base and exponent form a pair. You can chose any positive base and that will determine the exponent.243 = 49^1.5 that is base = 49, exponent = 1.5)or 243 = 10^2.5353 (approx) or 243 = 7^3.
base
54
5^4
5^4
yes. 5 x 5 x 5 x 5 = 625
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 of an exponent is the main number. For example in 56 the number 5 is the base and 6 is the exponent.
4 is the base, 2 is the exponent.
If you have ab then a is the base and b the exponent
10x 10 is Base & x is 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)
For 104 the base is 10 and the exponent is 4.
in a problem like n4=625 you need to do a mult-step equations In the example, 4log n = log 625 log n = (log 625)/4 n = 10^[(log 625)/4] = 5 Although this particular answer is obvious, you could also solve n5=625, or any other power of n, which isn't, using this method. hope that it is helpful to you!