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Solve for x and steps would be appreciated!

UpTheChels  Nov 3, 2017
edited by UpTheChels  Nov 3, 2017

Best Answer 

 #2
avatar+78762 
+3

log2 x  + log2 3 = log 2 2 + log2 9

 

We can write

 

log2 (3x)  = log2 (2*9)   the logs are the same....so we can solve

 

3x  = 2*9

 

3x  = 18      divide both sides by 3

 

x  = 6

 

 

cool cool cool

CPhill  Nov 3, 2017
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2+0 Answers

 #1
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+1

Solve for x:
(log(x))/(log(2)) + (log(3))/(log(2)) = 1 + (log(9))/(log(2))

 

Rewrite the left hand side by combining fractions. (log(x))/(log(2)) + (log(3))/(log(2)) = (log(x) + log(3))/(log(2)):
(log(x) + log(3))/(log(2)) = 1 + (log(9))/(log(2))

 

Multiply both sides by log(2):
log(x) + log(3) = log(2) + log(9)

 

Subtract log(3) from both sides:
log(x) = log(2) - log(3) + log(9)

log(2) - log(3) + log(9) = log(2) + log(1/3) + log(9) = log(2) + log(1/3) + log(9) = log((2 9)/3) = log(6):
log(x) = log(6)

 

Cancel logarithms by taking exp of both sides:
x = 6

Guest Nov 3, 2017
 #2
avatar+78762 
+3
Best Answer

log2 x  + log2 3 = log 2 2 + log2 9

 

We can write

 

log2 (3x)  = log2 (2*9)   the logs are the same....so we can solve

 

3x  = 2*9

 

3x  = 18      divide both sides by 3

 

x  = 6

 

 

cool cool cool

CPhill  Nov 3, 2017

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