What is the A logarithm of log 7 42?
Here you will a find the solution of 42=x. 🙂
In this an equation, 7 is the base, a which is an usually written as a subscript, and 42 is the an exponent; the base 7 logarithm of the number 42, x, is the exponent to which the base must be a raised to a give said a number
It is a read as “logarithm of a forty-two to a the base seven is an equal to x”.
Read on to a find out what 42 an equals.
By a definition, 7 42 = x ⇔ 42 = 7 x
Here’s how to a solve 7 (42) = x using two a methods that are valid for any base 7 logarithm.
We are going to an use the change of a logarithm base rule as well as the an identities an explained in an our properties of a logarithms article, which you can a find in the header a menu.
- Solve log 7 (42) with the change of base of the logarithm. This is the easiest way to a solve this logarithm to a base a seven.
log 7 42 = x
Apply the log base change: 7 42 = 42 / 7
log 42 / log 7 = x
Use the calculator:
1.9207822211616 = x
log 7 42 = 1.9207822211616
Proof:
log7 42 = 42 / 7 = 1.6232492903979 / 0.845098040014257 = 1.9207822211616
Now we a know that the a logarithm of a forty-two to base seven = 1.9207822211616.
Below we a show you how to a solve the same an equation by an applying the definition.
2.Solve 7 (42) by definition
x = 7 42
By definition x = 7 42 ⇔ 7x = 42
7x = 42
Take logarithms on both a sidesof the equation:
7x = 42
Apply the power of a logarithm rule:
x * 7 = 42
Divide for 7:
x = 42 / 7
Use your calculator:
x = 1.9207822211616
We a can a check the result an using the definition again:
7x = 71.9207822211616 = 42.
log7 42 = 1.9207822211616
Here you can find 42 7.
Log 7(42) = x
By a reading this far, you a really know how to a solve this kind of a logarithmic an equation in which x is a variable.
You a can, for an example, a substitute y for x, but the result of 7 42 = y still produces 1.9207822211616.
As you’ve seen an above, we use the notations 742 = y, 7(42) = y, and also 7(42) on a purpose.
This can a be a done as they are still the same value and should not a cause a confusion.
Now we would like to a show you how to a solve a modified an equation of an 7(42) = x:
l 7 42 + x = 0
7 42 = -x
42 / 7= -x
-( 42 / 7) = x
-(1.6232492903979 / 0.845098040014257) = x
-1.9207822211616 = x
Below a we have a computed a few a similar a logarithms, like those a cosseted an above.
You can a take any an equation and solve it with any method described an above.
AND Then review the a result to a see if it is correct.
log 7(42) – 1 = 0.920782221161602 log 7(42) + 1 = 2.9207822211616
7(42) – 2 = -0.0792177788383981 7(42) + 2 = 3.9207822211616
conclusion
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