Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Answer:
D. log₁₀ 1,000.
E. log₃ 27
Step-by-step explanation:
Logarithms
Logarithms are the inverse equations of their exponential counterparts.
In an exponential equation, it finds the value of an exponent made a base and power.
In a logarithm equation, it finds the value of the power that produces an exponent with a certain base.
In other words,
[tex]b^x=c[/tex]
[tex]log_b(c)=x[/tex].
Knowing that logs are inverses of exponents can help evaluate them.
[tex]\hrulefill[/tex]
Solving the Problem
To determine the correct answers, we must find the value of [tex]log_2=8[/tex].
This logarithm means that when 2 is raised to some power x, it produces 8.
[tex]2^x=8[/tex]
Knowing 8 to be the cube value of 2,
[tex]x=3 \rightarrow log_2(8)=3[/tex].
Now, we have to find answer choices where their value is also 3.
[tex]\dotfill[/tex]
Narrowing Down the Answer Choices
Using the facts mentioned in the top section, we can rewrite all of the logarithms as exponents.
[tex]A)\: 5^x=20\\\\B)\: 10^x=125\\\\C)\: 10^x=100\\\\[/tex]
[tex]D)\: 10^x=1000\\\\E)\: 3^x=27\\\\F)\: 10^x=0.001\\[/tex]
No power that raises 5 will get 20, so we can eliminate A.
The same can be said for B.
100 is the squared value of 10, meaning that x = 2. This isn't the same as the solution x = 3, so C is crossed off.
1000 is the cubed value of 10, meaning x = 3. So, D is a correct answer.
Same thing with E, 27 is the cubed value of 3, so E is also correct.
0.001 or [tex]\dfrac{1}{1000}[/tex] is the same as [tex]10^-^3[/tex], meaning x = -3. Not 3, so F is wrong.
Thus, D and E are our final answers.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.