Properties of exponents and logs problem

In summary, the conversation involves finding the value of B from the given equations. The properties of exponents are used to rewrite the equations and solve for B, resulting in a correct answer of 7/4.
  • #1
fatcrispy
24
0
Find B when given: Y = log2B and 2y+4 + 4y+3 = 224

I could use some help figuring out the process to this. Thanks
 
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  • #2


the log of a number is the power to which the base is raised to give that number

so if z=ab then b=logaz
 
  • #3


I'm still having trouble. 2y=z and y+4=log2Z and y+3=log4R? What do I do with this? Could you help me solve it please I am kind of lost.

I get Z + R = 224 and B = 2Y Now what?
 
  • #4


You need to remember some properties of exponents:

xa+b = xa·xb
xab = (xa)b

Also, it can help to rewrite 4 as 22.

When you can rewrite the equation with 2y, replace them with B and then solve for B.
 
  • #5


Ok so I got a funky answer.

2y24+22y26=224
B=2y So,
16B+64B2=224
4B2+B=14

I ended up with B=-2 but that doesn't make sense with -2=2y
 
  • #6


That's only one (extraneous) root of the quadratic equation you got. The other one is the correct answer.
 
  • #7


Ah 7/4 thanks!
 

Related to Properties of exponents and logs problem

1. What is an exponent?

An exponent is a number that represents how many times a base number is multiplied by itself. It is written as a superscript to the right of the base number, such as 23 where 2 is the base and 3 is the exponent.

2. How do you simplify expressions with exponents?

To simplify an expression with exponents, you can use the rules of exponents. If the bases are the same, you can add the exponents. If the exponents are being multiplied, you can multiply them. If the exponent is a negative, you can rewrite it as a fraction with a positive exponent. If the exponent is 0, the answer is always 1.

3. What is the difference between a logarithm and an exponent?

A logarithm is the inverse operation of an exponent. While an exponent represents repeated multiplication, a logarithm represents the power to which a base number must be raised to get a certain value. For example, in the expression log28 = 3, the logarithm is 3 and the base is 2.

4. How do you solve logarithmic equations?

To solve a logarithmic equation, you can use the properties of logarithms to rewrite the equation in a simpler form. Then, you can use inverse operations to isolate the variable. Remember to check your solutions, as some equations may have extraneous solutions.

5. How are exponents and logarithms used in real life?

Exponents and logarithms are used in many fields of science, such as chemistry, physics, and biology. They are also used in finance, engineering, and computer science. For example, in chemistry, logarithms are used to measure pH, and in finance, they are used to calculate compound interest. In computer science, they are used in algorithms and data compression.

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