Could someone check my answers?

25. 32^(2x-3)=2

Answer- x= 8/5

26. 9^(2x+1)=81

Answer- x= 1/2

27. 1/4=2^3x

Answer- x= -2/3

28. 1/27=3^2x

Answer- x= -3/2

29. 9^x=27

Answer- x= 3/2

30. 32^x=4

Answer- x= 2/5

31. 27^(x+1)=9

Answer- x= 1/2

32. 125^(x-2)=25

Answer- x= 7/2

33. 81^(x-1)=27^2x

Answer- x= -2

34. 4^(3x-7)=32^2x

I'm having problems with number 34.

34.

4^(3x-7) = 32^x
(2^2)^(3x-7) = (2^5)^x
2^(6x-14) = 2^(5x)

6x - 14 = 5x
x = 14

#31 and #32 are also incorrect, the rest are good

31.

27^(x+1) = 9
(3^3)^(x+1) = 3^2
3^(3x+3) = 3^2
3x+3=2
x = -1/3

32.

125^(x-2)x = 25
(5^3)^(x-2) = 5^2
5^(3x-6) = 5^2
3x-6=2
3x = 8
x = 8/3

Thank you

To solve question number 34, we can rewrite the equation using the properties of exponents. Let's begin:

34. 4^(3x-7) = 32^(2x)

First, we can express 32 as a power of 2:

32 = 2^5

Now we can substitute 32 in the equation:

4^(3x-7) = (2^5)^(2x)

Using the property (a^b)^c = a^(b*c), we simplify the equation:

4^(3x-7) = 2^(5*2x)

Next, we can simplify the exponents:

4^(3x-7) = 2^(10x)

Now, since the bases are the same, we can set the exponents equal to each other:

3x - 7 = 10x

To isolate the variable, let's subtract 3x from both sides of the equation:

-7 = 7x

Now divide by 7 on both sides:

-1 = x

The final answer is x = -1.

Please note that this is the solution for question number 34. If you need help with any other questions, feel free to ask!

To solve the equation in number 34, let's rewrite the bases of each exponent in terms of the same number. In this case, we can rewrite the equation as:

(2^2)^(3x-7) = (2^5)^2x

Now, we can simplify both sides of the equation:

2^(2(3x-7)) = 2^(5(2x))

Apply the power of a power property on both sides:

2^(6x-14) = 2^(10x)

Since the bases are equal, we can set the exponents equal to each other:

6x - 14 = 10x

Subtract 6x from both sides:

-14 = 4x

Divide both sides by 4:

x = -14/4

Simplify:

x = -7/2

Therefore, the answer to number 34 is x = -7/2.