To solve this inequality, we can start by rewriting the inequality with exponents instead of logarithms.
GivenLog2x(0.125) ≥ log2(64x-1)
This can be rewritten as2^(log2x(0.125)) ≥ 2^(log2(64x-1))
Now, we can simplify the exponents using the property of logarithms that statesIf loga(b) = c, then a^c = b
Using this property, we getx ≥ 64x - 1
Next, let's solve for xx - 64x ≥ --63x ≥ -x ≤ 1/63
Therefore, the solution to the inequality is x ≤ 1/63.
To solve this inequality, we can start by rewriting the inequality with exponents instead of logarithms.
Given
Log2x(0.125) ≥ log2(64x-1)
This can be rewritten as
2^(log2x(0.125)) ≥ 2^(log2(64x-1))
Now, we can simplify the exponents using the property of logarithms that states
If loga(b) = c, then a^c = b
Using this property, we get
x ≥ 64x - 1
Next, let's solve for x
x - 64x ≥ -
-63x ≥ -
x ≤ 1/63
Therefore, the solution to the inequality is x ≤ 1/63.