Exponential equation 7 * 3 ^ (x + 1) - 5 ^ (x + 2) = 3 ^ (x + 4) - 5 ^ (x + 3) Have a detailed process, mainly tell me how each step comes out. Don't just give me an answer

Exponential equation 7 * 3 ^ (x + 1) - 5 ^ (x + 2) = 3 ^ (x + 4) - 5 ^ (x + 3) Have a detailed process, mainly tell me how each step comes out. Don't just give me an answer

7*3^(x+1)-5^(x+2)=3^3*3^(x+1)-5*5^(x+2)7*3^(x+1)-5^(x+2)=27*3^(x+1)-5*5^(x+2)4*5^(x+2)=20*3^(x+1)4*5*5^(x+1)=20*3^(x+1)5^(x+1)=3^(x+1)(5/3)^(x+1)=1x+1=0x=-1

2X power of 1.5-23 * 5-50 = 0
X power of 2.2 * x power of 5 = 5 power of 0.1 (x-1 power of 10)
The x power of 3.2 + the x power of 2 + the x power of 2 + the x power of 2 + the x power of 2 + the x power of 3 = the x power of 3 + the x power of 3 + the x power of 1 + the x power of 3 + the x power of 2 + the x power of 3 + the x power of 3
4.5 to the power of X + 1 = 3 to the power of (x square minus one)
Lgx + 2 power of 5. X = 1000
6. The X-6 power of 125 under the root of degree 18 * 25 under the root of degree 2x = 0.2 under the root of degree 3x
Little brother, I just learned this thing... I really don't have a clue
Good answer, I will add points
You can answer as many questions as you like

These equations are exponential equations, we can use the method of substitution to solve them
1. Let the x power of 5 be y, then Y > 0
5Y ^ 2-23y-50 = 0
2.10^(x+1)=10^(5x-5)
x+1=5x-5
x=3/2
3. Multiply both sides by (3 / 2) ^ X
The equation is transformed into 1 + 2 + 4 + 8 = (9 / 2) ^ x + 3 * (9 / 2) ^ x + 9 * (9 / 2) ^ x + 27 * (9 / 2) ^ X
You can do it with the idea of substitution
6 are all logarithmic equations in disguise, so we can use the logarithmic property to do it
4. Take logarithm (x-1) * lg5 = (x ^ 2-1) Lg3 on both sides
X + 1 = LG (5 / 3) or X-1 = 0
X = LG (5 / 30) or x = 1
5. Take logarithm lgx (lgx + 2) = 3 on both sides
(lgx)^2+2lgx-3=0
(lgx+3)(lgx-1)=0
Lgx = - 3 or 1
X = 1 / 1000 or 10
6. The original formula can be reduced to 5 ^ [(X-6) / 6] * 5 ^ (1 / x) = 5 ^ (1 / - 3x)
Then the exponential operation is performed: (X-6) / 6 + 1 / x = 1 / - 3x
x^2-6x+6=-2
x^2-6x+8=0
X = 2 or 4

Find the linear equation satisfying the following conditions: (1) passing through the intersection of two lines 2x-3y + 10 = 0 and 3x + 4Y-2 = 0, and parallel to the line X-Y + 1 = 0;
(2) It passes through the intersection of two lines 2x + Y-8 = 0 and x-2y + 1 = 0 and is perpendicular to 3x-y-2 = 0

(1) Idea 1: find out the intersection point of two straight lines, and use point oblique to find out the equation of straight line
The second idea is to find out the intersection of two straight lines and substitute X - y + M = 0 to get the equation of straight line
Idea 3: let the equation of the straight line be (2x-3y + 10) + m (3x + 4Y-2) = 0, and use the equation parallel to X-Y + 1 = 0 to get M
(2) Similar to (1)