Find the value of [tex]x[/tex].
[tex]\log_x 8 = 0.5[/tex]
Answer (3)
0\ and\ x\neq1\\\\log_x8=0.5\iff x^{0.5}=8\ \ \ \ |square\ of\ both\ sides\\\\\left(x^{0.5}\right)^2=8^2\\\\x=64\\\\check:\\log_{64}8=0.5\iff64^{0.5}=8\to 64^\frac{1}{2}=\sqrt{64}=8"> D : x > 0 an d x ξ = 1 l o g x β 8 = 0.5 βΊ x 0.5 = 8 β£ s q u a re o f b o t h s i d es ( x 0.5 ) 2 = 8 2 x = 64 c h ec k : l o g 64 β 8 = 0.5 βΊ 6 4 0.5 = 8 β 6 4 2 1 β = 64 β = 8
The student is asking for the solution to the logarithmic equation log x (8) = 0.5. This equation means they are looking for a number x, such that x raised to the power of 0.5 is equal to 8.
To solve for x, we can rewrite the equation in exponential formβthis translates to x^{0.5 = 8
Solving for x:
βx = 8
x = 8Β²
x = 64
Therefore, the value of x is 64.
The value of x in the equation lo g x β 8 = 0.5 is 64 . We derived this by converting the logarithmic equation into an exponential equation and squaring both sides. Finally, we verified our solution by substituting it back into the original equation.
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