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Log 2 (x+5)-log 2 (2x-1)=5?

1 Answer

grace · Stefan V.

May 21, 2018

$x = \frac{37}{63}$ $x=37/63$

Explanation:

${log}_{2} (\frac{x + 5}{2 x - 1}) = 5$ $log_2 ((x+5)/(2x-1))=5" "$ (condense it)

$2^{5} = \frac{x + 5}{2 x - 1}$ $2^5 =(x+5)/(2x-1)" "$ ( $2 =$ $2=$ base, and it stays, log becomes exponent)

$\frac{32}{1} = \frac{x + 5}{2 x - 1}$ $32/1=(x+5)/(2x-1)" "$ (cross multiply $\to 32 \times (2 x - 1)$ $-> 32 xx (2x-1)$ )

$64 x - 32 = x + 5$ $64x-32=x+5 " "$ (simplify)

$63 x = 37$ $63x=37$

$x = \frac{37}{63}$ $x=37/63$

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