Study guides

☆

Q: How do you solve this logarithmic equation ln x equals 5?

Write your answer...

Submit

Still have questions?

Continue Learning about Trigonometry

-3 + ln(x) = 5 ln(x) = 8 eln(x) = e8 x = e8 x =~ 2981

AnswerLet x and y be any real numbers:log x = yx = log inv (y) = 10^yExample:pH =13.22 = -log [H+]log [H+] = -13.22[H+] = inv log (-13.22) = 10^(-13.22)[H+] = 6.0 x 10-14 MFINDING ANTILOGARITHMS using a calculator (also called Inverse Logarithm)Sometimes we know the logarithm (or ln) of a number and must work backwards to find the number itself. This is called finding the antilogarithm or inverse logarithm of the number. To do this using most simple scientific calculators,enter the number,press the inverse (inv) or shift button, thenpress the log (or ln) button. It might also be labeled the 10x (or ex) button.Example 5: log x = 4.203; so, x = inverse log of 4.203 = 15958.79147..... (too many significant figures)There are three significant figures in the mantissa of the log, so the number has 3 significant figures. The answer to the correct number of significant figures is 1.60 x 104.Example 6: log x = -15.3;so, x = inv log (-15.3) = 5.011872336... x 10-16 = 5 x 10-16 (1 significant figure)Natural logarithms work in the same way:Example 7: ln x = 2.56; so, x = inv ln (2.56) = 12.93581732... = 13 (2 sig. fig.)Application to pH problems:pH = -log (hydrogen ion concentration) = -log [H+] Example 8: What is the concentration of the hydrogen ion concentration in an aqueous solution with pH = 13.22? pH = -log [H+] = 13.22log [H+] = -13.22[H+] = inv log (-13.22)[H+] = 6.0 x 10-14 M (2 sig. fig.)

Related questions

-3 + ln(x) = 5 ln(x) = 8 eln(x) = e8 x = e8 x =~ 2981

The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)

ln 60 = a

A basic logarithmic equation would be of the form y = a + b*ln(x)

To be logarithmic the equation would be, ( otherwise just linear ) 3x + 7 = 20 subtract 7 from each side 3x = 13 now, you know the answer is between x = 2 and x = 3, so I use natural logs both sides ln(3x) = ln(13) as this is a logarithmic operation you can bring down the x in front of the ln sign on the left x ln(3) = ln(13) divideboth sides by ln(3) x = ln(13)/ln(3) ( not ln(13/3)!!!!! ) x = 2.334717519 -------------------------check in original equation 3(2.334717519) + 7 = 20 13 + 7 = 20 20 = 20 --------------checks

If the equation was ln(x) = 2.35 then x = 10.4856, approx.

hanks to the limitations of the browser through which questions are posted, it is not clear what the question is but, here goes: If the question was ea = 35, then the answer is a = ln(35) where ln are the natural logarithms.

5 + (-4) = 1 x = -4

3 ln(x) = ln(3x)ln(x3) = ln(3x)x3 = 3xx2 = 3x = sqrt(3)x = 1.732 (rounded)

There are many equations that are neither linear nor quadratic. A simple example is a cubic equation, such as y = x3, or a logarithmic equation, such as y = ln(x).

8958=e^(5x) ln both sides -> ln(8958)=5x Therefore x=1.82

y = a + b*log(x) or y = a + b*ln(x) where a and b are constants.

People also asked