+0

# Logarithmic equation help

0
348
2
+79

Solve for x and steps would be appreciated!

Nov 3, 2017
edited by UpTheChels  Nov 3, 2017

#2
+98125
+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

Nov 3, 2017

#1
+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

Nov 3, 2017
#2
+98125
+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

CPhill Nov 3, 2017