Common
The natural logarithm is calculated to base e, where e is Euler's constant. For any number, x loge(x) = log10(x)/log10(e)
logx(3) = log10(7) (assumed the common logarithm (base 10) for "log7") x^(logx(3)) = x^(log10(7)) 3 = x^(log10(7)) log10(3) = log10(x^(log10(7))) log10(3) = log10(7)log10(x) (log10(3)/log10(7)) = log10(x) 10^(log10(3)/log10(7)) = x
Logarithms are kind of like reverse exponents. log is just a quick way to write log10. loge can also be shortened to ln. Logarithm form, lobbN=L, can also be written as bL=N. For example, log39=2 because 32=9.
You can convert logarithms of different bases to the same base. After that, you may or may not be able to simplify the resulting expression. Example of change-of-base: log21024 = ln(1024) / ln(2) Instead of natural logarithms, you can convert to any other base: log21024 = log10(1024) / log10(2)
The logarithm function is defined so that if y = 10x then log y = x So, if x = 1, y = 101 = 10 and so log 10 = 1
The logarithm of 9 with base 10, aka log10 of 9 is approx. 0,954
The meaning of this subscript is the base of a specific logarithm; example: log10, the usual logarithm with the base 10.
The natural logarithm is calculated to base e, where e is Euler's constant. For any number, x loge(x) = log10(x)/log10(e)
No. Log x may be written more explicitly as log10(x). That is, the logarithm of x to the base 10. Assuming that In x is a misprint for ln x, this is loge(x) ie the logarithm of e to the base e. log10(x) = loge(x)/loge(10)
logx(3) = log10(7) (assumed the common logarithm (base 10) for "log7") x^(logx(3)) = x^(log10(7)) 3 = x^(log10(7)) log10(3) = log10(x^(log10(7))) log10(3) = log10(7)log10(x) (log10(3)/log10(7)) = log10(x) 10^(log10(3)/log10(7)) = x
Definition to use for the log (logarithm):the logarithm of a number (n) to a given base (b) is the exponent (e) to which the base must be raised in order to produce that number.(Raising to the power is the inverse of taking the logarithm.)logb(n) = e or be = nFor example, the logarithm of 1000 to base 10 is 3 ( log10(1000) = 3),because 10 to the power of 3 is 1000: 103 = 1000.-log10[H+] is (by definition) used to calculate the pH of a dilute solution in which [H+] = concentration of H+ (or H3O+) in mol/L.pH = -log10[H+] or [H+] = 10-pH
-6, assuming this is log10(0.000001)This means that 10x = 0.000001, x=-6
Acids, bases and neutrals The negative base-ten logarithm of the hydronium ion (H3O+) concentration or -log10[H3O+]
Logarithms are kind of like reverse exponents. log is just a quick way to write log10. loge can also be shortened to ln. Logarithm form, lobbN=L, can also be written as bL=N. For example, log39=2 because 32=9.
You can convert logarithms of different bases to the same base. After that, you may or may not be able to simplify the resulting expression. Example of change-of-base: log21024 = ln(1024) / ln(2) Instead of natural logarithms, you can convert to any other base: log21024 = log10(1024) / log10(2)
The pH is the co-logarithm of the activity of the dissolved ions H+ in a solution. The formula is (a is the activity):pH = - log10 aH
The logarithm function is defined so that if y = 10x then log y = x So, if x = 1, y = 101 = 10 and so log 10 = 1