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In this lesson were gonna 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 two raised to the X is equal to 16 now you might already see the answer, but I'm going to go ahead and solve it now we know that 2 to the fourth power is 16 so X is equal to 4 you can also do this log of 16 divided by log of 2 if you type that in that's equal to 4 which is X using the change of base form try this one log of X log base X of 81 is equal to 4 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 3 to the fourth is 81 now what about this one log base 5 of X is equal to 3 converts it to its exponential form 5 to the third is equal to X that's 5 times 5 times 5 5 times 5 is 25 and 5 quarters is a dollar 25 so 25 times 5 is 125 lets try some more examples log base 32 of X lets say its equal to 4 over 5 go ahead and try this one so 32 raised to the 4 over 5 is equal to X and what is that equal to what is 32 raised to the 4 over 5 how can we simplify this exponential fraction, so first you want to find the fifth root of 32 and then raise it to the fourth so what number multiplied it by itself five times is 32 two to the fifth power is 32 so 32 to the 15 is 2, so now we got to find out what 2 to the fourth is equal to 2 to the fourth is 16 and so X is 16 here's the next one log base 3 of 5x plus 1 is equal to 4 find the value of x so lets convert it to its exponential form 3 to the fourth is equal to what's inside and 3 to the fourth is 81 lets subtract both sides by 181 minus 1 is 80 and if we divide by 5 80 divided by 5 is 16, so that's the value of x if log X is equal to 24 what is the value of x now we don't have a base if there are no bases is written it's assumed to be base 10, so this is going to be 10 raised to the 24th which is a very, very big number, so I'm going to leave it as 10 to the 24th now what about this one Ln X is equal to 7 what is the value of x natural logs have the base e so e to the 7th is equal to X and that is the answer now if you want the decimal value X is approximately one thousand ninety 663 try this one log base seven x squared plus three X plus 9 is equal to two so lets convert it to its exponential form 7 raised to the second power is equal to what's inside that is its equal to x squared plus 3x plus 9 7 squared is 49 and let's subtract both sides by 9 so 40 is equal to x squared plus 3x lets move the 40 to the right side so x squared plus 3x minus 40 is equal to 0 now what two numbers multiply to negative 40 but add to 3 this is going to be 8 and negative 5, so this can be factored 2x plus 8 times X minus 5 so X is equal to negative 8 and positive 5 lets try this example the natural log of 3x minus 2 lets say its equal to 5 what is the...
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