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Veronika [31]
4 years ago
8

Solve the equation by using tu basic properties of logarithms log(2x)=3 (Picture provided)

Mathematics
1 answer:
serg [7]4 years ago
7 0

Answer:

Option b

Step-by-step explanation:

According to the property of sum of logarithms we know that

log(ab) = log(a) + log(b).

In this case we have the equation:

log(2x) = 3

Using the property of sum of logarithms:

log(2) + log(x) = 3

log(x) = 3 - log(2)

We also know that:

10 ^{(logx)} = x     -------- <em>Inverse logarithm</em>

So:

x = 10 ^{3-log(2)}

x = 500

Another easiest way to solve it is the following:

Make w = 2x.

Then:

log(2x) = log(w)

log(w) = 3

w = 10^3  -------- <em>Inverse logarithm property</em>

w = 1000  

but w= 2x. Then:

2x = 1000\\\\x = 500

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8x - (2x - 13) = 42<br>solve and check the equation​
pantera1 [17]

Answer:

x = 29/6

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Distributive Property

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

8x - (2x - 13) = 42

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. [Distributive Property] Distribute negative:                                                     8x - 2x + 13 = 42
  2. [Subtraction] Combine like terms:                                                                    6x + 13 = 42
  3. [Subtraction Property of Equality] Subtract 13 on both sides:                        6x = 29
  4. [Division Property of Equality] Divide 6 on both sides:                                 x = 29/6

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in <em>x</em>:                                                                                                  8(29/6) - [2(29/6) - 13] = 42
  2. Multiply:                                                                                                             116/3 - [29/3 - 13] = 42
  3. [Brackets] Subtract:                                                                                           116/3 - -10/3 = 42
  4. Subtract:                                                                                                            42 = 42

Here we see 42 does indeed equal 42.

∴ x = 29/6 is the solution.

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