help please..in solving this logarithmic equation

3 log_x 2  + log_x 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

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

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

 

3log_x2 + log_x18 = 2

 

log_x2³ + log_x18 = 2

 

log_x8 + log_x18 = 2

 

log_x(8*18) = 2

 

log_x144 = 2

 

144 = x²

 

x = 12