First, we can simplify the equation by rewriting 64 as 4^3:
4^5x - 10 = 4^3
Now, we can rewrite both sides of the equation with the same base:
2^(2*5x) - 10 = 2^(3)
Using the properties of exponents:
2^(10x) - 10 = 8
Now, substitute 8 as 2^3:
2^(10x) - 10 = 2^3
Now the bases are the same, so we can set the exponents equal to each other:
10x = 3
Divide by 10 on both sides:
x = 3/10
So, x = 0.3
Combine the two terms on the left side:
3^(2x - 4) = 21
Rewrite 21 as 3^3:
3^(2x - 4) = 3^3
Now, the bases are the same, so we can set the exponents equal to each other:
2x - 4 = 3
Add 4 to both sides:
2x = 7
Divide by 2 on both sides:
x = 7/2
So, x = 3.5
First, we can simplify the equation by rewriting 64 as 4^3:
4^5x - 10 = 4^3
Now, we can rewrite both sides of the equation with the same base:
2^(2*5x) - 10 = 2^(3)
Using the properties of exponents:
2^(10x) - 10 = 8
Now, substitute 8 as 2^3:
2^(10x) - 10 = 2^3
Now the bases are the same, so we can set the exponents equal to each other:
10x = 3
Divide by 10 on both sides:
x = 3/10
So, x = 0.3
3^(x-2) * 3^(x-2) = 21Combine the two terms on the left side:
3^(2x - 4) = 21
Rewrite 21 as 3^3:
3^(2x - 4) = 3^3
Now, the bases are the same, so we can set the exponents equal to each other:
2x - 4 = 3
Add 4 to both sides:
2x = 7
Divide by 2 on both sides:
x = 7/2
So, x = 3.5