by Guest » Fri Mar 29, 2024 8:12 am
To solve the equation 8^x+4^x=32, we can recognize that both 8 and 4 are powers of 2. Rewriting them in terms of 2, we have 2^3x+2^2x=2^5.
Now, notice that 32=2^5. So, we can rewrite the equation as 2^3x+2^2x=2^5.
This gives us 2^2x(2^x+1)=25.
Dividing both sides by 2^2x, we get 2^x+1=2^(5−2x).
Now, we see that the left-hand side is increasing while the right-hand side is decreasing as x increases.
Therefore, there's only one solution to this equation. By inspection, it's evident that x=1 satisfies the equation.
Hence, 8^1+4^1=32, fulfilling the condition
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