How would you solve this logarithmic equation?
I assume you meant to write log (subscript)b 3 = y. For this problem, you just need to know the log rules: log (a) + log (b) = log (ab) log (a) - log (b) = log (a/b) 18 = 3*3*2, so log(b) 18 = log (b) (2*3*3) = log (b) 2 + log (b) 3 + log (b) 3 = x + 2y 9/16 = (3*3)/(2*2*2*2), so log(b)(9/16) = log(b) 3 + log(b) 3 - log(b) 2 - log(b) 2 - log(b) 2 - log(b) 2 = 2y/4x = y/2x Hope that helps!
How do I solve the logarithmic equation.
I think this is what you mean (where I am using log7 to mean log to the base 7). Just read your additional comments so here is my new answer: log7(x) + log7 (x - 48) = 2 Use the fact that: log7(a) + log7(b) = log(ab) log7[x(x - 48)] = 2 Now use the fact that: log7(a) = b can be changed to a = 7^b x(x - 48) = 7^2 = 49 x^2 - 48x - 49 = 0 (x - 49)(x + 1) = 0 The answers are: x = 49 and x = -1 However x = -1 is not a good solution since x > 48 based on the second term of the original equation. Since we are taking log7 of (x - 48) x must be greater than 48 to get a valid log. The answer is x = 49 Check: log7(49) + log7(49 - 48) = log7(49) + log7(1) = 2 + 0 = 2 And the answer given above is correct
Explain how to solve exponential and logarithmic equations by graphing.?
graph plotting is a very good method to find solutions but u need to hve good graph plotting technique. first plot a good graph and find the points where figures are intersecting each other this point will be called a soution. for logarithm u need to first find its domain and then see where its nature changes like increasing or decreasing
4.Solve the given equation. (a). In x = 0.35 X=? (b). log x = 0.35 X=?
a) x = e^0.35 b) x = 10^0.35
Solve the logarithmic equation for x. (Enter your answers as a comma-separated list.) log2(x + 9) − log2(x − 9) = 3?
log2(x + 9) − log2(x − 9) = 3 : x ≠ -9, 9 log2[(x+9)/(x-9)] = 3 (x+9)/(x-9) = 8 x+9 = 8x - 72 x = 8x-81 -7x = -81 x = 81/7
TI-89 Titanium Solving Logarithmic Equations for x?
Do you know that "change of base" formula for logarithms? Most calculators do only base 10 (LOG button) and base e (LN button) logarithms. To do any other base, say "B", enter Log(x)/Log(B). For example the base 3 logarithm of 81 is 4: Log(81)/Log(3) = 4. ----- The standard graphing calculator equation solving procedure is: Graph both sides of the equation and use the "intersection" feature: On most calculators: Press "Y=" (diamond-f1 on a TI-89) and enter: Y1 = Log(x+1)/Log(3) - Log(x-2)/Log(5) Y2 = 2 Press the "Graph" button (diamond-f3 on a TI-89) and then use the "intersection" function ("F5" then "5" on a TI-89; "Calc" button on other TI's; and "G-Solv" on most Casio's). Follow the directions on screen, each brand is a little different. WARNING! This equation has more than one solution. It is very easy to overlook the other solution if you only look at the graph with the standard window. ----- Here is another cute way to solve that equation which works both on graphing and many non-graphing calculators: Solve for the one of the "X", perhaps first "x". ( Put both sides in the exponent of "5" to eliminate the base 5 logarithm, ( Multiply by (x-2), then raise both sides to the power of Log(3)/Log(5) and subtract 1: x = (25(x-2)) ^ (Log(3)/Log(5)) -1 On the calculator, enter a guess, perhaps "10", and press enter. Then type: (25*(ANS-2)) ^ (LOG(3)/LOG(5)) - 1 and press "enter" again and again and again until the answer stops changing. {It might take awhile. "10" is not a good guess!} The other solution can be found by solving for the other "x" value: x = ((x+1)/9) ^ (Log(5)/Log(3)) + 2
Find the solutions to the logarithmic equation: log2(x^2-2x-76)=2?
A logarithm is nothing more than an exponent. The expression on the left is nothing more than the exponent you need to raise 2 to produce the quantity in ( ). If you think of both sides as exponents to the base 2, you get from the properties of logarithms, the equation x^2 - 2x - 76 = 4. Now, solve the equation x ^2 - 2x - 80 = 0. This factors as (x - 10)(x + 8) = 0. Solving, you get x = -8, 10. However, you must make sure that the expression in ( ) is always > 0, Only - 8 satisfies that condition.