Question #484ea

Question

Question #484ea

1 Answer

Impact of this question

1927 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-07T16:06:47

$x = \frac{1 \pm \sqrt{65}}{8} = 1.13$ $x=(1+-sqrt65)/8=1.13$

Explanation:

$ln (x + 4) = {ln x}^{2} + ln (4)$ $ln(x+4)=lnx^2+ln(4)$ -> Use property ${log}_{b} a^{x} = x {log}_{b} a$ $log_ba^x=xlog_ba$
$ln (x + 4) = ln (4 x^{2})$ $ln(x+4)=ln(4x^2)$ ->Use property ${log}_{b} (x y) = {log}_{b} x + {log}_{b} y$ $log_b(xy)=log_bx+log_by$
$ln (x + 4) - ln (4 x^{2}) = 0$ $ln(x+4)-ln(4x^2)=0$ -> Put everything on one side
$ln (\frac{x + 4}{4 x^{2}}) = 0$ $ln((x+4)/(4x^2))=0$ ->Use property ${log}_{b} (\frac{x}{y}) = {log}_{b} x - {log}_{b} y$ $log_b(x/y)=log_bx-log_by$
$10^{0} = \frac{x + 4}{4 x^{2}}$ $10^0 = (x+4)/(4x^2)$ -> use definition $y = log x \Leftrightarrow 10^{y} = x$ $y=logx iff 10^y=x$
$1 = \frac{x + 4}{4 x^{2}}$ $1=(x+4)/(4x^2)$
$4 x^{2} = x + 4$ $4x^2=x+4$
$4 x^{2} - x - 4 = 0$ $4x^2-x-4=0$
$x = \frac{1 \pm \sqrt{1 - 4 (4) (- 4)}}{8}$ $x=(1+-sqrt(1-4(4)(-4)))/8$
$x = \frac{1 \pm \sqrt{65}}{8} = 1.13 or - 0.88$ $x=(1+-sqrt65)/8=1.13 or -0.88$

Science

Math

Humanities

... and beyond

Question #484ea

1 Answer

Explanation:

Related questions

Impact of this question