Respuesta :
Hello from MrBillDoesMath!
Answer:
See Discussion below
Discussion:
Let's number your equations:
1) 10^x+7=37
Subtract 7 from both sides
10^x = 37 - 7 = 30
Take log to base 10 ("log10") and note that log10 (10^x) = x. Hence
x = log10 (30)
which is approximately 1.5
2) -9×12^-m-9=-15
Add 9 to both sides:
-9 * 12^(-m) = -15 + 9 => -15 + 9 = -6
-9 * 12^(-m) = -6 => divide both sides by -9
12^(-m) = +6/9 = 2/3 => take log10 of each side
(-m) log10(12) = log10(2/3) => divide both sides by log10(12)
-m = log10(2/3) / log10(12) => multiply both sides by -1
m = -log10(2/3) / log10(12)
m = .163 (approximately)
3) log7 x+log7 2=1 => raise sides to the 7th power
7^ { (log(7)x) + (log(7)2) } = 7^1 => A^(m+n) = A^m * A^n
7^log(7)x * ( 7^log(7)2) = 7 => as 7 ^ (log(7)x) =x
x * 2 =7 => subtract 2 from both sides
x = 7/2
Thank you,
MrB
