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Answered

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can someone please help me solve this logarithm equation

Can Someone Please Help Me Solve This Logarithm Equation class=

Sagot :

bowmaian000

Answer:

[tex]x=\frac{33}{7}[/tex]

Step-by-step explanation:

Orginal equation:

[tex]log_2(x+1)-log_2(x-4)=3[/tex]

So lets do this step by step.

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

This gives us:

[tex]log_2(x+1)=3+log_2(x-4)[/tex]

Then, when we put this into exponential form, we get:
[tex]2^{3+log_2\left(x-4\right)}=\left(x+1\right)[/tex]

This then equals:

[tex]8(x-4) = x-1[/tex]

This can be simplfied into:

[tex]8x-32 = x+1[/tex]

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:

[tex]7x=33[/tex]

Finally, we can divide 33 by 7 to get:
[tex]x=\frac{33}{7}[/tex]

Hope this helps! :3

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