Mathematics, 30.06.2019 12:30, rayanne6050

Let logb(2) = 0.3869, logb(3) = 0.6131, and logb(5) = 0.8982. using these values, evaluate logb(1/6).

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answered: campbellkruger

The value is -1

Step-by-step explanation:

We use two properties of logarithms: (1) an exponent of the argument can be written as factor of the log, (2) log of a product of two terms is the sum of log of each term:

$\log_b \frac{1}{6}=\log_b 6^{-1}=-1\cdot \log_b 6=-\log_b(2\cdot 3)=\\= -(\log_b 2 + \log_b 3)=-(0.3869+0.6131)=-1$

answered: Guest

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the (original price) is $420.

0.7x = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

answered: Guest

4 puzzles in 3 hours

step-by-step explanation:

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Let logb(2) = 0.3869, logb(3) = 0.6131, and logb(5) = 0.8982. using these va...