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Mathematics

1 answer:

Alja [10]3 years ago

3 0

<h3>Answer: x = 6</h3>

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Work Shown:

$\log_{4}(x+10)+\log_{4}(x-2)=\log_{4}(64)\\\\\log_{4}\left((x+10)(x-2)\right)=\log_{4}(64)\\\\(x+10)(x-2)=64\\\\x^2-2x+10x-20=64\\\\x^2-2x+10x-20-64=0\\\\$

$x^2+8x-84=0\\\\(x+14)(x-6)=0\\\\x+14=0 \ \text{ or } \ x-6=0\\\\x=-14 \ \text{ or } \ x=6\\\\$

Those are the possible solutions, but plugging x = -14 back into the original equation will lead to an error. So we rule x = -14 out

x = 6 works as a solution however

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4 years ago

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hodyreva [135]

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The length of KH is 6 units and OH is 6.3 units.

Step-by-step explanation:

Given the figure with lengths LO=5 and OK=4. we have to find the length of OH and KH.

In ΔLOH

By Pythagoras theorem

$LH^2=LO^2+OH^2\\\\LH^2=5^2+OH^2$ → (1)