SOLUTION: solve this {{{ log(3,sqrt(x-5)) = 2 }}} I try to solve like this log3 (x-5)^1/2 - log3 5/2 = log3 9 x^1/2 - 5/2 = 9 x^1/2 = 23/2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve this {{{ log(3,sqrt(x-5)) = 2 }}} I try to solve like this log3 (x-5)^1/2 - log3 5/2 = log3 9 x^1/2 - 5/2 = 9 x^1/2 = 23/2      Log On


   

Question 858777: solve this +log%283%2Csqrt%28x-5%29%29+=+2+
I try to solve like this
log3 (x-5)^1/2 - log3 5/2 = log3 9
x^1/2 - 5/2 = 9
x^1/2 = 23/2
Found 2 solutions by solver91311, josgarithmetic:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!






If if and only if , therefore:



Square both sides and solve the resulting single variable linear equation.

John

My calculator said it, I believe it, that settles it
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Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Base was not stated. Assuming base is 10.

log%2810%2C3sqrt%28x-5%29%29=2
log%2810%2C3%2Asqrt%28x-5%29%29=2
10%5E2=3sqrt%28x-5%29
100=3%2Asqrt%28x-5%29
100%2F3=sqrt%28x-5%29
%28100%2F3%29%5E2=x-5
x=%28100%2F3%29%5E2%2B5
x=10000%2F9%2B45%2F9
highlight%28x=10045%2F9%29
OR
highlight%28x=1116%261%2F9%29