Question 1153449
two properties of logs are applicable here.


first is :


ln(x^a) = a * ln(x)


second is:


ln(x * y / z) = ln(x) * ln(y) - ln(z)


first gets you:


a * ln(y) = ln(y^a)


b * ln(z) = ln(z^b)


your formula starts with:


ln(x) + a * ln(y) - b * ln(z)


applying the first property above makes the expression above equivalent to:


ln(x) + ln(y^a) - ln(z^b)


second gets you:


ln(x * y^a / z^b) = ln(x) + ln(y^a) - ln(z^b)


here's a reference on properties of logarithms.


the log log function in your calculator is log(x) to the base of 10.


the ln function is log(x) in your calculator is log(x) to the base of e.


the properties of logs applies to both log function and ln function.


here's a couple of references on the properties of logs.


<a href = "http://www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP-1-19_RESOURCE/U18_L2_T2_text_final.html" target = "_blank">http://www.montereyinstitute.org/courses/DevelopmentalMath/TEXTGROUP-1-19_RESOURCE/U18_L2_T2_text_final.html</a>


<a href = "https://www.purplemath.com/modules/logrules.htm" target = "_blank">https://www.purplemath.com/modules/logrules.htm</a>