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STEP 1: Replace the function notation f (x) by y. f (x) y. STEP 2: Switch the roles of x and y. STEP 3: Isolate the log expression on one side (left or right) of the equation. STEP 4: Convert or transform the log equation into its equivalent exponential equation.
0:00 1:28 Suggested clip How to find the inverse of a logarithmic function, f(x) = log2 (x YouTubeStart of suggested client of suggested clip How to find the inverse of a logarithmic function, f(x) = log2 (x
A logarithm is the inverse of an exponent. The equation log x = 100 is another way of writing 10x = 100. This relationship makes it possible to remove logarithms from an equation by raising both sides to the same exponent as the base of the logarithm.
0:00 1:28 Suggested clip How to find the inverse of a logarithmic function, f(x) = log2 (x YouTubeStart of suggested client of suggested clip How to find the inverse of a logarithmic function, f(x) = log2 (x
Logarithms are the “opposite” of exponential, just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs “undo” exponential. Technically speaking, logs are the inverses of exponential. On the left-hand side above is the exponential statement “y = bx”.
Step 1: bring all the logs on the same side of the equation and everything else on the other side. Step 3: Exponential to cancel the log (run the hook). Step 4: Solve for x. Step 5: Check your answer. Step 1: Take logs of both sides using one of the given bases.
Logarithms are the “opposite” of exponential, just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs “undo” exponential. Technically speaking, logs are the inverses of exponential. On the left-hand side above is the exponential statement “y = bx”.
We know that the inverse of a log function is an exponential. So, we know that the inverse of f(x) = log sub(x) is f^-1(y) = by. If the base is e, and we are dealing with the natural log, then the inverse of f(x) = LN(x) is f^-1(y) = EAY.
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