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
kakasveta [241]
2 years ago
5

Condense the following logs into a single log:

Mathematics
1 answer:
mamaluj [8]2 years ago
7 0

QUESTION 1

The given logarithm is

8\log_g(x)+5\log_g(y)

We apply the power rule of logarithms; n\log_a(m)=\log_(m^n)

=\log_g(x^8)+\log_g(y^5)

We now apply the product rule of logarithm;

\log_a(m)+\log_a(n)=\log_a(mn)

=\log_g(x^8y^5)

QUESTION 2

The given logarithm is

8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)

We apply the power rule of logarithm to get;

=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)

We apply the product to obtain;

=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)

We apply the quotient rule; \log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )

=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})

=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})

You might be interested in
Cos²x - 2 sin²x = -2 .Help me to solve it ​
Alex777 [14]

Step-by-step explanation:

note that

sin²x = (1-cos²x)

LHS= cos²x - 2 sin²x

= cos²x - 2(1-cos²x)

= cos²x - 2 + 2cos²x

= 3cos²x - 2

or

cos²x = (1-sin²x)

LHS= cos²x - 2 sin²x

=1-sin²x - 2 sin²x

= 1-3sin²x

7 0
3 years ago
Given: ∆ABC, AB = CB BD − median to AC E∈ AB ,F∈ BC AE = CF Prove: △ADE ≅ △CDF ΔBDE ≅ ΔBDF
NemiM [27]

Answer:

1) By SAS theorem, ΔADE≅ΔCDF

2) By SSS theorem, ΔBDE≅ΔBDF

Step-by-step explanation:

Consider isosceles triangle ABC (see diagram).

1. In triangles ADE and CDF:

  • AD≅DC (since BD is median, then it divides side AC in two congruent parts);
  • AE≅CF (given);
  • ∠A≅∠C (triangle ABC is isosceles, then angles adjacent to the base are congruent).

By SAS theorem, ΔADE≅ΔCDF.

2. In triangles BDE and BDF:

  • side BD is common;
  • DE≅DF (ΔADE≅ΔCDF, then congruent triangles have congruent corresponding sides);
  • BE≅FB (triangle ABC is isosceles, AB≅BC, AE≅CF, then BE=AB-AE, FB=BC-CF).

Be SSS theorem, ΔBDE≅ΔBDF.

7 0
3 years ago
Solution to this inequality? <br> 3(5+2n) &gt; 7 +10n<br> Please show work , Thank you
vodka [1.7K]
3(5+2n) \ \textgreater \  7 +10n \\ \\ 15 + 6n \ \textgreater \  7 + 10n \\ \\ 15 \ \textgreater \  7 + 10n - 6n \\ \\ 15 \ \textgreater \  7 + 4n \\ \\ 15 - 7 \ \textgreater \  4n \\ \\ 8 \ \textgreater \  4n \\ \\  \frac{8}{4} \ \textgreater \  n \\ \\ 2 \ \textgreater \  n \\ \\ n \ \textless \  2 \\ \\

The final result is: n < 2.
7 0
2 years ago
Read 2 more answers
Quadrilateral QRST has diagonals that are perpendicular but not congruent. Which type of quadrilateral could describe quadrilate
Serggg [28]

Answer: rhombus

Step-by-step explanation: because trump is the best president

8 0
3 years ago
Adrian and his children went into a restaurant where they sell hotdogs for $3 each
prohojiy [21]

Answer: 16x + 4y= 80

16 (3) + 4 (8) = 80

5 0
2 years ago
Other questions:
  • Geometry Question, I’m really super duper confused here
    6·1 answer
  • What steps would you take to compare 2 kilograms and 3,200 grams m
    13·2 answers
  • Which of these terms does not describe polygon abc ?
    10·1 answer
  • What 2 factors can be multiplied to give 120 and added or subtracted to give 7​
    14·1 answer
  • What is 9+10 plz show work <br> the right one will get brainly
    11·1 answer
  • Evaluate -6-2x when x=-4
    15·1 answer
  • The product of 3 and r
    6·2 answers
  • You buy 25 pounds of tomatoes need 1.7 ounces how many portions can be made
    9·2 answers
  • The following represents slopes of two lines. Which answer choice describes the two lines? m = 7 and m = -7
    6·1 answer
  • If you start off with 1220 and you take away 100 then add 50 how much do you have
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!