1)5^(3x-1)=8 2)4^(5x+2)=9

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1) To solve the first equation, we can rewrite 8 as 2^3. So the equation becomes:
5^(3x-1) = 2^3

Now we can rewrite 5 as 2^(log2(5)) to have the same base:
(2^(log2(5)))^(3x-1) = 2^3

Using the properties of exponents, we can simplify this to:
2^(log2(5) * (3x-1)) = 2^3

Since the bases are the same, the exponents must be equal:
log2(5) * (3x-1) = 3

Now we can isolate x by solving for it:
3x - 1 = 3 / log2(5)
3x = 3 / log2(5) + 1
x = (3 / log2(5) + 1) / 3

2) To solve the second equation, we can rewrite 9 as 3^2. So the equation becomes:
4^(5x+2) = 3^2

Now we can rewrite 4 as 2^2:
(2^2)^(5x+2) = 3^2

Using the properties of exponents, we can simplify this to:
2^(2 * (5x+2)) = 3^2

Since the bases are the same, the exponents must be equal:
2 * (5x+2) = 2

Now we can isolate x by solving for it:
10x + 4 = 2
10x = 2 - 4
10x = -2
x = -2 / 10
x = -1/5