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TiliK225 [7]
3 years ago
13

Express each of the following in logarithmic form ​

Mathematics
2 answers:
worty [1.4K]3 years ago
8 0

\text{Use the exponent-to-log rule: }\quad y=b^x\quad \rightarrow \quad log_b\ (y)=x

(i) Answer:   \bold{3=log_5 (125)}

<u>Step-by-step explanation:</u>

5^3=125\qquad \rightarrow \qquad 3=log_5 (125)

(ii) Answer:   \bold{-2=log_{3} \bigg(\dfrac{1}{9}\bigg)}

<u>Step-by-step explanation:</u>

3^{-2}=\dfrac{1}{9}\qquad \rightarrow \qquad -2=log_3 \bigg(\dfrac{1}{9}\bigg)

(iii) Answer:   \bold{-3=log (0.001)}

<u>Step-by-step explanation:</u>

10^{-3}=0.001\qquad \rightarrow \qquad -3=log_{10} (0.001)

\text{Note: }log_{10}\text{ is generally written without the subscript.}\\\text{It is similar to writing an exponent of 1. We would write }x^1\text{ as x}.\\\text{We write }log_{10}(y)\text{ as log(y)}

(iv) Answer:   \bold{\dfrac{3}{4}=log_{81} (27)}

<u>Step-by-step explanation:</u>

81^{\dfrac{3}{4}}=27\qquad \rightarrow \qquad \dfrac{3}{4}=log_{81} (27)

vodomira [7]3 years ago
5 0

Answer:

See explanation.

Step-by-step explanation:

(i)  5^3 = 125

log 5^3 = log 125

Using the rule log a^n = n log a

3 log 5 = log 125.

(ii) 3^-2 = 1/9

-2 log 3 = log 1/9

(iii)   10^-3 = 0.001

-3 log 10 = log 0.001

(iv)   81^3/4 = 27

3/4 log 81 = log 27.

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Step-by-step explanation:

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List five rational numbers between -4/5 and -2/3 . Please tell by step by step explaintion ​
attashe74 [19]

9514 1404 393

Answer:

  -0.67, -0.68, -0.69, -0.70, -0.71

Step-by-step explanation:

There are an infinite number of ways to do this.

Perhaps the simplest is to do it in decimal.

 -4/5 = -0.8

  -2/3 = -0.666... (repeating 6)

Any negative decimal number between these values will do. For example, ...

  -0.67, -0.68, -0.69, -0.70, -0.71

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If you want to choose fractions that are evenly spaced between the given values, you can find their difference, then divide that difference into 6 parts (1 more than the number of numbers you need).

  -2/3 -(-4/5) = 4/5 -2/3 = (12 -10)/(5·3) = 2/15 . . . . length of interval

  1/6 of this difference is ...

     (1/6)(2/15) = 2/90 = 1/45

The interval end point nearest 0 is ...

  -2/3 = -30/45

so the 5 intermediate values will be that value with -1/45 repeatedly added:

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_____

<em>Additional comment</em>

The fractions we came up with could be referred to as "5 arithmetic means between -2/3 and -4/5." There is nothing in the problem statement suggesting the values need to be evenly spaced.

When doing this in decimal, you can obtain a new value simply by adding more digits to the decimal fraction:

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Step-by-step explanation:

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3 years ago
A store marks up all of their merchandise by 70%. The floor price of a scarf is $117.25.
KiRa [710]

Answer:

  $68.97

Step-by-step explanation:

Markup is the difference between the cost of an item and the price at which it is sold:

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Here, the markup is said to be 70%. The base for that percentage can be either the cost price or the selling price. The way this question is worded suggests the markup is 70% of the cost price.

So, we have ...

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or

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__

Then, to find the cost price, we can divide by its coefficient in this equation. Doing that gives ...

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The store's purchase price before the markup for this item was $68.97.

4 0
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The letters a,b and c, represent nonzero constants. Solve ax+b=c for x
insens350 [35]

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x = \frac{c-b}{a}

Step-by-step explanation:

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Now divide by a on both sides. This means that to solve for x the equation must be ...

x = \frac{c-b}{a}

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