SOLUTION: Using the properties of logarithms which single term does not contain a logarithm: e^ln(3x^5). (1)3x^5, (2)x^15 (3) x^8 or (4) x^5/3?

Algebra.Com
Question 202905: Using the properties of logarithms which single term does not contain a logarithm: e^ln(3x^5). (1)3x^5, (2)x^15 (3) x^8 or (4) x^5/3?
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

Here are two solutions:
  1. If you really understand what logarithms represent then the answer is obvious. In general represents "the exponent one could put on 'a' to get 'x'. In your problem you have which represents "the exponent one could put on 'e' to get "". And where do we find ? As an exponent on 'e'! So is, by the very definition and meaning of logarithms: !
  2. Let's say the . Now let's find the ln of both sides:

    Using the property we can rewrite the right side:

    The ln(e) is 1 so now we have

    Since the ln's are equal, the arguments must be equal:

    Substituting back in for y using we get:
RELATED QUESTIONS

E^2-4ln(x)+ln(y) Use the the properties of logarithms to write the following... (answered by josgarithmetic)
Use the properties of logarithms to write the following expression as a single term that... (answered by lwsshak3)
Use the properties of logarithms to write the following expression as a single term that... (answered by Alan3354)
Use properties of logarithms to rewrite the expression as a single logarithm.... (answered by greenestamps)
Use the properties of logarithms to write the expression log6(x + 5) + 1/2 log6 x as (answered by MathLover1)
Using laws of logarithms, write the expression below using sums and/or differences of... (answered by rothauserc)
use the properties of logarithms to write the single logarithm as a sum and/or difference (answered by jsmallt9)
how to write the logarithms as a single logarithm with a coefficient of one. ln 2 + 6 ln (answered by Alan3354)
Use the properties of logarithms to write the expression 3log(x+8)-2log(x-5) as a single... (answered by stanbon)