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# log4(x+2)=3

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log4(x+2)=3

How do I solve this?

Guest Apr 26, 2017
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#1
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After you get the answer, try looking at different rules. This stuff will catch you by suprise, as some college teachers like to bring in out of to test.

Veteran  Apr 26, 2017
#2
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log4(x+2)=3

A)

$$log(4(x+2))=3\\10^3=4(x+2)\\4x+8=1000\\x=\frac{1000-8}{4}\\\color{blue}x=248$$

B)

$$log(4 )\cdot (x+2)=3\\log\ 4=\frac{3}{x+2}\\x+2=\frac{3}{log\ 4}\\x=\frac{3}{log\ 4}-2\\\color{blue}x=2.98289214233$$

C)

$$log_4(x+2)=3\\4^3=x+2\\x=4^3-2\\\color{blue}x=62$$

!        Look for a solution.

asinus  Apr 26, 2017
edited by asinus  Apr 26, 2017
#3
+1

Solve for x:
(log(x + 2))/(log(4)) = 3

Multiply both sides by log(4):
log(x + 2) = 3 log(4)

3 log(4) = log(4^3) = log(64):
log(x + 2) = log(64)

Cancel logarithms by taking exp of both sides:
x + 2 = 64

Subtract 2 from both sides: