Can some i get some with solving exponential and logarithmic equations

Hello from MrBillDoesMath!

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

3/6   and 9/18

step-by-step explanation:

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!