Answer:
x=75
Step-by-step explanation:
2 * ln (e ^ ln (2x)) - ln (e ^ ln (10x)) = ln (30)
Apply exponent rules
2 * ln (2x) - ln (10x) = ln (30)
Apply log rules
2 * ln (2x) - ln (10x) = ln (30)
Apply log rule: logc(ab) = logc(a) +logc (b)
Apply exponent rules
2 * ln (2x) - ln (10x) = ln (30)
Apply log rules
2 * ln (2x) - ln (10x) = ln (30)
Apply log rule: logc(ab) = logc(a) + logc (b)
ln (2x) = ln (2) + ln (2)
2(ln (2) + ln (x)) - ln (10x) = ln (30)
Apply log rule: logc(ab) = logc(a) + logc (b)
ln (10x) = ln (10) + ln (x)
ln (2x) = ln (2) + ln (2)
2(ln (2) + ln (x)) - ln (10x) = ln (30)
Apply log rule: logc(ab) = logc(a) + logc (b)
ln (10x) = ln (10) + ln (x)
Apply log rule: logc(ab) = logc(a) + logc (b)
ln (10x) = ln (10) + ln (x)
2(ln(2)+ln(x))-(ln(10)+ln(x))=]
Expand 2(ln(2) +ln(x)
ln (x) + 2 * ln (2) - ln (10) = ln (30)
Subtract 2 * ln (2) - ln (10) from both sides
In(x) + 2ln(2) - In(10) - (2ln(2) - In
Simplify
ln (x) = ln (30) - 2 * ln (2) + ln (10)
Simplifify ln (30) - 2 * ln (2) + ln 10
ln (x) = ln (75)
Apply log rule: If logb(f(x)) = logb (g(x)) then f(x) = g(x)
x = 75
Verify Solutions: X = 75
Check the solutions by plugging them
into 2 * ln (2x) - ln (10x) = ln (30) Remove the ones that don't agree with the equation.
Plug in x =75
2 * ln (2 * 75) - ln (10 * 75) = ln (30)
2 * ln (2 * 75) - ln (10 * 75) = ln (30)
ln (30) = ln (30)
True
