How do you solve ln(5-2x^2)+ln9=ln43?

3 Answers
Sonnhard ยท Jacobi J.
May 27, 2018

x=pm1/3

Explanation:

We have
ln(5-2x^2)=ln(43)-ln(9)

ln(5-2x^2)=ln(43/9)

so

5-2x^2=43/9

5-43/9=2x^2

2/9=2x^2

1/9=x^2

F. Javier B.
May 27, 2018

See explanation below

Explanation:

The goal is to get a expresion logA=logB. By inyectivity of logarithm we arrive to A=B

In our case: ln(5-2x^2)+ln9=ln43

ln(5-2x^2)=ln43-ln9=ln43/9

Then 5-2x^2=43/9 or equivalent

5-43/9=2x^2

2/9=2x^2

1/9=x^2

x=+-1/3

It is obvious that both solution are valid

marfre
May 27, 2018

x = +- 1/3

Explanation:

Given: ln (5 - 2x^2) + ln 9 = ln 43

Use the logarithm property ln a + ln b = ln (a*b)

ln ((5 - 2x^2)9) = ln 43

ln (45 - 18x^2) = ln 43

Exponentiate both sides and use the logarithm property e^ln x = x

e^(ln (45 - 18x^2)) = e^(ln 43)

45 - 18x^2 = 43

45 - 43 = 18x^2

2 = 18 x^2

2/18 = 1/9 = x^2

x = +- 1/3

CHECK to see if the answers work in the problem (must be ln of a positive number)#:

ln (5-2(1/3)^2) = ln (5-2/9) > 0

ln (5-2(-1/3)^2) = ln (5-2/9) > 0

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