SOLUTION: Please help me solve for x. {{{ log( 2, x ) + 4log( x, 2 ) = 5 }}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me solve for x. {{{ log( 2, x ) + 4log( x, 2 ) = 5 }}}      Log On


   

Question 836162: Please help me solve for x. +log%28+2%2C+x+%29+%2B+4log%28+x%2C+2+%29+=+5+
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2Cx%29%2Blog%28x%2C2%5E4%29=5
log%282%2Cx%29%2B%28log%282%2C2%5E4%29%29%2F%28log%282%2Cx%29%29=5, used change of base formula.
Multiply both sides by log(2,x)
%28log%282%2Cx%29%29%5E2%2Blog%282%2C2%5E4%29=5%2Alog%282%2Cx%29
.
highlight_green%28%28log%282%2Cx%29%29%5E2-5%2Alog%282%2Cx%29%2B4=0%29

Temporarily substitute highlight_green%28u=log%282%2Cx%29%29 and solve first for u, according to your knowledge of quadratic equations; and then finish getting to x.




-
log%28a%2Cx%29=log%28b%2Cx%29%2Flog%28b%2Ca%29
The Change of Base formula