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in this lesson were going to focus on solving basic logarithmic equations lets start with this one log base 2 of 16 is equal to x go ahead and find the value of x what we need to do is convert it to exponential form 2 raised to the x is equal to 16. now you might already see the answer but im going to go ahead and solve it now we know that 2 to the 4th power is 16. so therefore x is equal to four you can also do this log of 16 divided by log of two if you type that in thats equal to four which is x using the change of base formula try this one log of x log base x of 81 is equal to four what is x so lets convert it to its exponential form x to the fourth is 81. so now lets find the value of x to do that we need to take the fourth root of both sides so the fourth root of 81 is equal to 3 because three to the fourth is eighty-one now what about this one log base five of x is equal to three convert it to its exponential form five to the third is equal to x thats five times five tim

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The Definition of a Logarithm Just as subtraction is the inverse operation of addition, and taking a square root is the inverse operation of squaring, exponentiation and logarithms are inverse operations. Finding an antilog is the inverse operation of finding a log, so is another name for exponentiation.

9:24 25:26 Solving Logarithmic Equations - YouTube YouTube Start of suggested clip End of suggested clip We need to use this equation to combine the two logs into a single log. So if log base 2 of x plusMoreWe need to use this equation to combine the two logs into a single log. So if log base 2 of x plus log base 2 of x plus 4 is equal to 5 then log base 2 of x times x plus 4.

Any exponential equation of the form ab=c can be written in logarithmic form using loga(c)=b. For example, the exponential equation 23=8 is written as log2(8)=3 in logarithmic form. The number after the equals sign in logarithmic form is the power that the base of the log is raised to to make the number inside the log.

The equation x = 2y is often written as a logarithmic function (called log function for short). The logarithmic function for x = 2y is written as y = log2 x or f(x) = log2 x. The number 2 is still called the base. Logarithmic FormExponential Formlog5 5 = 151 = 54-1 =10-2 = 0.012 more rows

The word logarithm, abbreviated log, is introduced to satisfy this need. This equation is rewritten as y = log 2 x. This is read as y equals the log of x, base 2 or y equals the log, base 2, of x. which is read y equals the log of x, base b or y equals the log, base b, of x.

Solving Logarithmic Equations Step 1: Use the rules of exponents to isolate a logarithmic expression (with the same base) on both sides of the equation. Step 2: Set the arguments equal to each other. Step 3: Solve the resulting equation. Step 4: Check your answers. Solve.

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.

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