1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lora16 [44]
3 years ago
15

Solve 9^x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b.

Mathematics
1 answer:
Sauron [17]3 years ago
6 0

Answer:

If you meant 9^x+4=11, then the answer is approximately 0.866.

If you meant 9^{x+4}=11, then the answer is approximately -2.909 which looks like what you meant based on the choices.

Step-by-step explanation:

9^x+4=11

First step is to get the exponential part by itself. The part that has the variable exponent which is the 9^x term.

To do this we need to subtract 4 on both sides:

9^x=11-4

Simplify:

9^x=7

The equivalent logarithmic form is:

\log_9(7)=x

I always say to myself the logarithm is the exponent that is how I know what to put opposite the side containing the log.

Anyways if you don't have options for computing \log_b(a) in your calculator you need to use the change of base formula.

\frac{\log(7)}{\log(9)}=x

So x \approx 0.8856

I don't see this as a choice so maybe you actually meant the following equation:

9^{x+4}=11

Let's see if this is the correct interpretation.

So the exponential part is already isolated.

So we just need to put in the equivalent logarithmic form:

\log_9(11)=x+4

Now we subtract 4 on both sides:

\log_9(11)-4=x

Again if you don't have the option for computing \log_b(a) in your calculator, you will have to use the change of base formula:

\frac{\log(11)}{\log(9)}-4=x

x \approx -2.909

You might be interested in
Can a triangle have sides of lengths 9,17,15? Show why or why not.
Elden [556K]

Answer:

A triangle has 3 sides: a, b, c satisfying inequalities below:

=> a + b > c > |a - b|

=> b + c > a > |b - c|

=> c + a > b > |c - a|

9, 15, 17 satisfy the inequalities above (you can check it easily).

Hope this helps!

:)

6 0
3 years ago
In the figure, three line segments cross at a common point. Angle A is 45°, and angle E is 85°. What is the measurement of angle
katen-ka-za [31]

Answer: Measure angle H = 42°


Step-by-step explanation:

"In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two non-adjacent angles to the exterior angle"

In given we have,

angle E is an exterior angle to triangle DFH

The two non-adjacent angles to angle E are angles D and H

Based on the above rule,

measure angle E = measure angle D + measure angle H

We are given this:

angle E = 87°

angle D = 45°

Substitute with the givens in the above rule and solve for the measure of angle H as follows:

angle E = angle D + angle H

87° = 45° + measure angle H

measure angle H = 87° - 45°

measure angle H = 42°

Hope this helped!

5 0
2 years ago
What is the value of b in the equation (y Superscript b Baseline) Superscript 4 Baseline = StartFraction 1 Over y Superscript 24
shusha [124]

The value of b is -6.

Explanation:

The expression is \left(y^{b}\right)^{4}=\frac{1}{y^{24}}

To determine the value of b, we shall solve the expression.

Applying exponent rule, \left(a^{b}\right)^{c}=a^{b c}, we get,

y^{4b}=\frac{1}{y^{24}}

Applying exponent rule, \frac{1}{a^{b}}=a^{-b}, we have,

y^{4b}=y^{-24}

The expression is of the form, a^{f(x)}=a^{g(x)} then f(x)=g(x)

Applying this rule, we get,

4b=-24

Dividing both sides by 4, we have,

b=-6

Hence, the value of b is -6.

4 0
3 years ago
Read 2 more answers
Find the quotient.
never [62]

Answer:

48÷3=16

Step-by-step explanation:

In the expression, 96 divided by 8 = a , the quotient a =12

. Divide 12 lizards into 6 equal groups. How many lizards are in each group?

There are2

lizards in each group.

5 0
3 years ago
Read 2 more answers
What percent of 16 is 0.12?
valentinak56 [21]

Answer:

0.75%

Step-by-step explanation:

Convert the fractions and then multiply by 100.

5 0
3 years ago
Read 2 more answers
Other questions:
  • What is the value of x?
    6·1 answer
  • Which is equivalent to the following expression?
    14·2 answers
  • QUIZ
    6·1 answer
  • #7 You sign up for 18 weeks
    6·1 answer
  • Need help on geometry
    6·2 answers
  • How many halves are in one and one-half?
    12·2 answers
  • An equilateral triangle has a perimeter of 15x3 33x5 feet. what is the length of each side?
    6·2 answers
  • Carol has 7 rolls of pennies containing 50 coins each, 11 rolls of nickels containing 40 coins each, 3 rolls of dimes containing
    7·1 answer
  • A swimmer speeds up 1.9 m/s to 3.8 m/s during the last 11.0 seconds of the race. What is the acceleration of the swimmer?
    7·1 answer
  • If y= 2x-3 were chnged to y=2x+5 how would the graph of the new function compare with the original
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!