Question
Asked Apr 2, 2019
9 views
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION.)
log 3 x + log(x + 5) = log 3(x + 32)
help_outline

Image Transcriptionclose

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION.) log 3 x + log(x + 5) = log 3(x + 32)

fullscreen
check_circle

Expert Answer

Step 1

A property:

The following are two properties of logarithm of two numbers, m and n at a given base, say c:

fullscreen
Step 2

Calculation:

Here, the base of the logarithm is c = 3; the numbers are m = x, n = x + 32.

fullscreen
Step 3

Note:

The logarithm of a non-positive quantity is not defined. The log function is defined only for positive numbers.

For x = –8, the left hand side (LHS) of the given equation would have the terms:

log3 x = log3 –8;

log3 (x + 5) = log3 (–8 + 5) = log3 &ndash...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Functions

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Help with #9

A: For a given curve r(t), the tangential component aT and the normal component aN are given by express...

question_answer

Q: All boxes with a square base, an open top, and a volume of 210 ft cubed have a surface area given by...

A: Approach:As a first step we will differentiate the given function and equate it to zero to find all ...

question_answer

Q: Please help.

A: The given series is,

question_answer

Q: Suppose you are standing in a field near a straight section of railroad tracks just as the locomotiv...

A: As a first step, let's convert the given information in a diagram. Please see the white board.Let A ...

question_answer

Q: how do i get number 3

A: Expanded the expression of f(x) first then used the exponent rule to find the derivatives. 

question_answer

Q: The beginning of the question is attached.  How do I argue that f(x) is concave if and only if g(x)=...

A: A function is concave or ceonvex is defined by the sign of its double derivative.A function is conve...

question_answer

Q: Determine the area, in square units, of the region bounded by g(x)=6x+12 and f(x)=x2 +7x−8 over the ...

A: We have to find the area under the curve of g(x), then substract the area under the curve of f(x). T...

question_answer

Q: A train is initially traveling at a rate of 5 miles per hour. The acceleration of the train is 5 mil...

A: Given: The acceleration of the train is 5 miles per hour squared. That is, a(t) = 5.The initial velo...

question_answer

Q: The funciton f in the figure satisfies the lim f(x)=5 as x approaches 4.  Determine the maximum valu...

A: (A) From the inequality |f(x)-5|<1 , we\'ll find range of f(x) first.