Use the following steps to prove that log b xy = log b x + log b

Question:

Use the following steps to prove that log_b xy = log_b x + log_b y.

a. Let x = b_p and y = b^q. Solve these expressions for p and q, respectively.

b. Use property E1 for exponents to express xy in terms of b, p, and q.

c. Compute log_b xy and simplify.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

See More Books

Question Posted: Jan 22, 2019 07:29 AM

Use the following steps to prove that log b x z = z log b x. a. Let x = b p . Solve this expression for p. b. Use property E3 for exponents to express x z in terms of b and p. c. Compute log b x z...
The points P, Q, R, and S, joined by the vectors u, v, w, and x, are the vertices of a quadrilateral in R 3 . The four points neednt lie in a plane (see figure). Use the following steps to prove that...
Prove the quadrilateral property in Exercise 83, assuming the coordinates of P, Q, R, and S are P(x 1 , y 1 , 0), Q(x 2 , y 2 , 0), R(x 3 , y 3 , 0), and S(x 4 , y 4 , z 4 ), where we assume that P,...
Draw a simple undirected graph G that has 12 vertices, 18 edges, and 3 connected components.
Given the Inventory Turnover (based on a 365-day year) (Cost of Goods Sold divided by Average Inventories ) is 9.78; and the Number of Days' Sales in Inventory (Inventory at Year-End divided by...
Compare the acquisition of Pfizer over Medivation company, with acquisition of Novartis over The Medicines Company? Is the role of acquisitions (size and type) similar for Novartis and Pfizer? Do...
A stock with current value $S(0)=100$ has an expected growth rate of its logarithm of $u=12 \%$ and a volatility of that growth rate of $\sigma=20 \%$. Find suitable parameters of a binomial...
Solar Energy Corp. has $4 million in earnings with four million shares outstanding. Investment bankers think the stock can justify a P/E ratio of 21. Assume the underwriting spread is 5 percent. What...
Two lakes are located on the same river, as shown in Figure 11-6. A is upstream of B. Water flows into A at a rate SA; it evaporates from A at a rate EA and from B at a rate EB. A tributary flows...
The duobinary, ternary, and bipolar signaling techniques have one common feature: They all employ three amplitude levels. In what way does the duobinary technique differ from the other two?
Assume that b > 0 and b 1. Show that log 1/b x = - log b x.
Modify the proof outlined in Exercise 84 and use property E2 for exponents to prove that log b (x/y) = log b x - log b y.
Pour some dry sand into a tin can with a cover. Compare the temperature of the sand before and after you vigorously shake the can for a couple of minutes. Predict what occurs. What is your...
What can you conclude about the acquisitions of property, plant, and equipment from this evidence?
Your organization is planning to purchase a new office building five years from now. The building will cost $3,000,000, have a useful life of 25 years, and have no salvage value. If your organization...
Omar bought a term life insurance policy nine years ago and converted it to a permanent policy last year. Yesterday, Omar committed suicide. Omar bought a term life insurance policy nine years ago...
Lorie is a healthy 60 year-old who owns a cottage by the lake with an unrealized capital gain of $200,000. She assumes the cottage value will continue to rise. Lorie believes that on her death she...
Impressions, views, click through rate, cost per click, landing page visits, revenue per visitor engagement metrics for high-value customers. email open rates, click through rates, dwell times, and...
How does a weighted moving average forecast differ from a simple moving average forecast?
As of January 1, 2018, Room Designs, Inc. had a balance of $9,900 in Cash, $3,500 in Common Stock, and $6,400 in Retained Earnings. These were the only accounts with balances in the ledger on January...
The cost (in dollars) of producing units of a certain commodity is C(x) = 5000 + 10x + 0.05 x2. (a) Find the average rate of change of C with respect to when the production level is changed (i) From...
The cost of producing x ounces of gold from a new gold mine is C = f(x) dollars. (a) What is the meaning of the derivative f'(x)? What are its units? (b) What does the statement f'(800) = 17 mean?...
Let T'(t) be the temperature (inoF) in Phoenix hours after midnight on September 10, 2008. The table shows values of this function recorded every two hours. What is the meaning of T'(8)? Estimate its...
Oak Creek Furniture Factory (OCFF), a custom furniture manufacturer, uses job order costing to track the cost of each customer order. On March 1, OCFF had two jobs in process with the following...
Image transcription text 9:10 X Test_Belgeleme_Vak... Q E .. . Yapisal Test ve Validasyon Takimi Test Belgeleme Muhendisligi Aday Vaka Calismasi Ad: Soyad: 1) Asagidaki sekilde, kok noktasindan...
Individual Key Learning Report Individual Key Learning Report A+ Individual Report on Key Learnings Students are required to prepare an individual report at the end of the semester to present the...

Use the following steps to prove that log b xy = log b x + log b

Question:

Step by Step Answer:

a Given x b p we have p log ...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions