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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 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.

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay.

To convert from exponential to logarithmic form, we follow the same steps in reverse. We identify the base b, exponent x, and output y. Then we write x=logb(y) x = l o g b ( y ) .

0:01 25:26 Solving Logarithmic Equations - YouTube YouTube Start of suggested clip End of suggested clip So therefore x is equal to four you can also do this log of 16 divided by log of two if you typeMoreSo 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.

log: (in math) An abbreviation for logarithm. logarithm: The power (or exponent) to which one base number must be raised multiplied by itself to produce another number. For instance, in the base 10 system, 10 must be multiplied by 10 to produce 100. So the logarithm of 100, in a base 10 system, is 2.

1:01 15:35 Logs and Exponentials - YouTube YouTube Start of suggested clip End of suggested clip And were doing it of eight. And we get three. So do you get comfortable with the fact that a lot isMoreAnd were doing it of eight. And we get three. So do you get comfortable with the fact that a lot is just another way of expressing. An exponential power its just writing in a different order.

LOGARITHMIC EQUATIONSDefinitionAny equation in the variable x that contains a logarithm is called a logarithmic equation.Recall the definition of a logarithm. This definition will be important to understand in order to be able to solve logarithmic equations.ExamplesEXAMPLES OF LOGARITHMIC EQUATIONSLog2 x = -518 more rows

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.

Exponential to log form is a common means of converting one form of a mathematical expression to another form. The exponential form ax=N a x = N is transformed and written in logarithmic form as LogaN=x L o g a N = x .

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.

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