The m power of 2 = the n power of 5 = 10 to find m + n

The m power of 2 = the n power of 5 = 10 to find m + n

Because 2 ^ m = 5 ^ n = 10
So m = log (210) n = log (510) (log (210) means 2 is the logarithm of base 10, log (510) means 5 is the logarithm of base 10)
So m + n = log (210) + log (510) = 1 / LG2 + 1 / lg5 = 1 / (LG2 * lg5)

Is the nth power of a? (the m power of a) is the nth power of a? (the a power of B) is the m power of a?

N-th radical a
a^n
b^m/a^m

Brothers, when to use the real number and imaginary number of the complex number Z in the mathematics of grade two in senior high school?
When m is a number, z = (m ^ 2 + m-2) + (m ^ 2 + 5m-6) I
1 real number 2 imaginary number 3 pure imaginary number?

When the imaginary part m ^ 2 + 5m-6 = 0, the solution is m = 1, or M = - 6, it is a real number
When the imaginary part m ^ 2 + 5m-6 is not equal to 0, that is, M is not equal to - 2 and M is not equal to 1, it is an imaginary number
If the real part m ^ 2 + m-2 = 0, that is m = - 2 or M = 1
At the same time, the imaginary part is not zero
That is, M = - 2 is a pure imaginary number

It is known that the complex z = x (1 + I) - Y (2 + I) is a pure imaginary number (x, y belongs to R), and | Z | = 1.1) to find the complex Z 2) to find the value of Z | 1-I |

(1) From the meaning of the question, z = x (1 + I) - Y (2 + I) = x + xi-2y-yi = (x-2y) + (X-Y) I because the complex Z is a pure imaginary number, so x-2y = 0, X-Y ≠ 0, that is, x = 2Y and X ≠ y. in addition, from | Z | = 1, we can get 2x ^ 2-6xy + 5Y ^ 2 = 1 by expanding (x-2y) ^ 2 + (X-Y) ^ 2 = 1 and substituting x = 2Y to get 8y ^ 2-12y ^ 2 + 5Y ^ 2 = 1 to get y = 1 or - 1 when y = 1