Given log_5 2≈0.4308 and log_527≈2.0478, evaluate the expressions. Note: you must use the given values and not values obtained from a calculator for those logarithms.
log_5 3
log_5 (27/50)
Answer :
Final answer:
To evaluate the expression log5 3, we can use the given values of log5 2 and apply the change of base formula. To evaluate log5 (27/50), we need to rewrite 27/50 as powers of 5 and use the properties of logarithms.
Explanation:
To evaluate the expression log5 3, we will use the fact that the logarithm of a number is the exponent to which the base must be raised to obtain that number. Since we are given the logarithm of 2 as log5 2 ≈ 0.4308, we can express 3 as a power of 2 by multiplying the exponent by log5 2: log5 3 = log5 (2x) where 2x = 3.
Therefore, x = log2 3. To evaluate this, we can use the change of base formula: log2 3 = log5 3 / log5 2.
Simplifying using the given logarithm values, we have log2 3 ≈ log5 3 / 0.4308.
To evaluate the expression log5 (27/50), we need to express 27/50 as powers of 5. Using the facts that 27 = 33 and 50 = 2 * 52, we can rewrite the expression as log5 (33 / (2 * 52)).
Using the properties of logarithms, we can simplify this expression to log5 (33) - log5 2 - log5 (52).
Finally, using the given logarithm values, log5 (27/50) ≈ 3 - 0.4308 - 2.0478.
Learn more about Evaluating logarithmic expressions here:
https://brainly.com/question/31828691
#SPJ11
The solutions to the logarithm equations are;
1) Log₅3 = 0.6826
2) Log₅(27/50) = -0.383
How to solve logarithm Equations?
There are different rules of logarithm such as;
Product rule which is; Log a + Log b = Log (ab)
Quotient rule which is; Log a - Log b = Log(a/b)
Power rule which is; Log aˣ = x log a
We are given that;
Log₅2 = 0.4308
Log₅27 = 2.0478
We know that 27 = 3³. Thus;
Log₅27 = Log₅3³
Using power rule, we have;
Log₅3³ = 3Log₅3
Thus;
Log₅27 = 3Log₅3 = 2.0478
1) We want to solve Log₅3
We have;
3Log₅3 = 2.0478
Thus;
Log₅3 = 2.0478/3 = 0.6826
2) Log₅(27/50)
Using quotient rule, we have;
Log₅27 - Log₅50
This can also be expressed as;
Log₅3³ - Log₅ (25 * 2)
= 3Log₅3 - [2Log₅5 + Log₅2]
= 2.0478 - 2 - 0.4308
= -0.383
Read more about Logarithm Equations at; https://brainly.com/question/237323
#SPJ1