The sum of the digits of a two-digit number is 8. If the digits are interchanged ,new number is 10 more than double the original number. Find the original number. pls help me I want ans with full process

Original number 26.

Step-by-step explanation:

xy - two-digit number

1) x + y = 8

2) Original two-digit number can be written as

10*x + y

3) If the digits interchanged yx,

then the new number can be written as

10*y + x

4)  Double the original number is

2*(10*x + y)

5) New number is 10 more than double the original number

(10*y + x) - (2*(10*x + y)) = 10

6) Now we have the system of 2 equations:

x + y = 8

(10*y + x) - (2*(10*x + y)) = 10 > 10y + x - (20x + 2y) = 10 ---> 8y - 19x = 10

x = 8 - y

8y - 19(8 - y) = 10

8y - 152 +19y = 10

27y = 162

y = 6

x = 8 - y = 8 - 6 = 2

x = 2

So, x =2, y = 6.

Original number 26.

Check:

Original number 26.

New number 62.

Double of the original number = 2*26= 52.

New number is 10 more than double the original number :

62 - 52 = 10 True

answer: 5

step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752