Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Rewrite the following in the form log(c). log(3)+log(4)

Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(3)+log⁡(4) \log (3)+\log (4)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Evaluate logarithms using propertiesright chevron icon

Full solution

Q. Rewrite the following in the form log⁡(c) \log (c) .\newlinelog⁡(3)+log⁡(4) \log (3)+\log (4)
  1. Identify property for combining logarithms: log⁡(3)+log⁡(4)\log(3) + \log(4)\newlineIdentify the property that can be used to combine the two logarithms.\newlineSum of logarithms of two numbers equals the logarithm of their product.\newlineProduct property: log⁡(P)+log⁡(Q)=log⁡(P×Q)\log(P) + \log(Q) = \log(P \times Q)
  2. Apply product property to combine logarithms: log⁡(3)+log⁡(4)\log(3) + \log(4)\newlineApply the product property of logarithms to combine the two logs into one.\newlinelog⁡(3)+log⁡(4)=log⁡(3×4)\log(3) + \log(4) = \log(3 \times 4)
  3. Calculate product of numbers: Calculate the product of 33 and 44.\newline3×4=123 \times 4 = 12
  4. Substitute product into logarithm: Substitute the product back into the logarithm. log⁡(3×4)=log⁡(12)\log(3 \times 4) = \log(12)
  5. Verify simplified form of expression: Verify that the expression is simplified and in the form log⁡(c)\log(c).\newlineThe expression log⁡(12)\log(12) is indeed in the form log⁡(c)\log(c) where c=12c = 12.

More problems from Evaluate logarithms using properties

Question
Evaluate.\newline56÷94= \frac{5}{6} \div \frac{9}{4}=
Get tutor helpright-arrow

Posted 3 months ago

Question
Evaluate.\newline83÷53= \frac{8}{3} \div \frac{5}{3}=
Get tutor helpright-arrow

Posted 3 months ago

Question
Evaluate.\newline54÷35= \frac{5}{4} \div \frac{3}{5}=
Get tutor helpright-arrow

Posted 3 months ago

Question
Evaluate.\newline34÷34= \frac{3}{4} \div \frac{3}{4}=
Get tutor helpright-arrow

Posted 3 months ago

Question
Write the expression in exponential form.\newline6×6×6×6×6= 6 \times 6 \times 6 \times 6 \times 6=
Get tutor helpright-arrow

Posted 3 months ago

Question
Write the expression in exponential form.\newline9×9×9×9×9×9×9= 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9=
Get tutor helpright-arrow

Posted 3 months ago

Question
The value of Vishal's car is depreciating exponentially.\newlineThe relationship between V V , the value of his car, in dollars, and t t , the elapsed time, in years, since he purchased the car is modeled by the following equation.\newlineV=22,500⋅10−t12 V=22,500 \cdot 10^{-\frac{t}{12}} \newlineHow many years after purchase will Vishal's car be worth $10,000 \$ 10,000 ?\newlineGive an exact answer expressed as a base−10-10 logarithm.\newlineyears
Get tutor helpright-arrow

Posted 3 months ago

Question
A scientist measures the initial amount of Carbon−14-14 in a substance to be 2525 grams.\newlineThe relationship between A A , the amount of Carbon−14-14 remaining in that substance, in grams, and t t , the elapsed time, in years, since the initial measurement is modeled by the following equation.\newlineA=25e−0.00012t A=25 e^{-0.00012 t} \newlineIn how many years will the substance contain exactly 2020 grams (g) (\mathrm{g}) of Carbon−14-14?\newlineGive an exact answer expressed as a natural logarithm.\newlineyears
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following is equivalent to log⁡7(a)⋅log⁡b(7) \log _{7}(a) \cdot \log _{b}(7) ?\newlineChoose 11 answer:\newline(A) log⁡(7) \log (7) \newline(B) log⁡(7a) \log (7 a) \newline(C) log⁡a(b) \log _{a}(b) \newline(D) log⁡b(a) \log _{b}(a)
Get tutor helpright-arrow

Posted 3 months ago

Question
Which of the following is equivalent to log⁡(a)⋅log⁡a(5) \log (a) \cdot \log _{a}(5) ?\newlineChoose 11 answer:\newline(A) log⁡(a) \log (a) \newline(B) log⁡(5) \log (5) \newline(C) log⁡(5a) \log (5 a) \newline(D) log⁡a(5a) \log _{a}(5 a)
Get tutor helpright-arrow

Posted 3 months ago

View all (34)