Question

Solving Exponential and Logarithmic Equation In exercise,solve for x or t.See example 5 and 6.

Answer 1

Answer:

$x=\frac{6e^3}{e^3-1}$

Step-by-step explanation:

$ln x - ln(x - 6) = 3$

Apply natural log property

ln mn=ln m + ln(n), ln(m/n)=ln(m)-ln(n)

$ln x - ln(x - 6) = 3$

$ln(\frac{x}{x-6} )=3$

All natural log has base 'e'

$\frac{x}{x-6} =e^3$

cross multiply

$x=e^3(x-6)$

$x=e^3x-6e^3$

add 6e^3 on both sides and -x on both sides

$6e^3=e^3x-x$

$6e^3=x(e^3-1)$

Divide e^3-1 on both sides

$x=\frac{6e^3}{e^3-1}$