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# help please..in solving this logarithmic equation

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3 log+ logx 18 = 2

Mar 3, 2020

#1
+26006
+2

3 logx 2  + logx 18 = 2       change to log10

3 log 2/log x    +    log 18/logx   = 2

3 log 2   + log 18 = 2 log x

3/2 log 2  + 1/2 log 18 = log x

1.07918 = log x

x = 12

Mar 3, 2020
#2
+2

This is the way I interpreted your question:

Solve for x:
(3 log(2))/log(x) + log(18)/log(x) = 2

Bring (3 log(2))/log(x) + log(18)/log(x) together using the common denominator log(x):

(3 log(2) + log(18))/log(x) = 2

Take the reciprocal of both sides:
log(x)/(3 log(2) + log(18)) = 1/2

Multiply both sides by 3 log(2) + log(18):

log(x) = 1/2 (3 log(2) + log(18)) Evaluate the RHS

Log(x) = 1.0791812460                Raise the RHS to the power of 10

x = 10^1.0791812460

x = 12

Mar 3, 2020
#3
+30637
+3

Another way of doing this using the property of logarithms is as follows:

3logx2 + logx18 = 2

logx23 + logx18 = 2

logx8 + logx18 = 2

logx(8*18) = 2

logx144 = 2

144 = x2

x = 12

Mar 3, 2020