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Can someone please help me solve this logarithm equation

Can someone please help me solve this logarithm equation-example-1
User Joce
by
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1 Answer

5 votes

Answer:


x=(33)/(7)

Explanation:

Orginal equation:


log_2(x+1)-log_2(x-4)=3

So lets do this step by step.

First, lets add
log_2(x-4) to both sides of the equation!

This gives us:


log_2(x+1)=3+log_2(x-4)

Then, when we put this into exponential form, we get:

2^(3+log_2\left(x-4\right))=\left(x+1\right)

This then equals:


8(x-4) = x-1

This can be simplfied into:


8x-32 = x+1

Then we can add 32 to both sides, and subtract x from both sides to get the variable and number each on their owns ide:


7x=33

Finally, we can divide 33 by 7 to get:

x=(33)/(7)

Hope this helps! :3

User Verax
by
8.1k points

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