41.0k views
4 votes
Please help me! Its for my big test tomorrow!

Please help me! Its for my big test tomorrow!-example-1
User Ricky Mo
by
7.9k points

1 Answer

4 votes

QUESTION 11

Given :
\ln(3x-8)=\ln(x+6)

We take antilogarithm of both sides to get:


3x-8=x+6

Group similar terms to get:


3x-x=6+8

Simplify both sides to get:


2x=14

Divide both sides by 2 to obtain:


x=7

12. Given;
\log_3(9x-2)=\log_3(4x+3)

We take antilogarithm to obtain:


(9x-2)=(4x+3)

Group similar terms to get:


9x-4x=3+2


5x=5

We divide both sides by 5 to get:


x=1

13.
\log(4x+1)=\log25

We take antilogarithm to get:


(4x+1)=25

Group similar terms


4x=25-1


4x=24

Divide both sides by 4


x=6

14. Given ;
\log_6(5x+4)=2

We take antilogarithm to get:


(5x+4)=6^2

Simplify:


(5x+4)=36


5x=36-4


5x=32

Divide both sides by 5


x=(32)/(5)

Or


x=6(2)/(5)

15. Given:
\log(10x-7)=3

We rewrite in the exponential form to get:


(10x-7)=10^3


(10x-7)=1000


10x=1000+7


10x=1007

Divide both sides by 10


x=(1007)/(10)

16. Given:
\log_3(4x+2)=\log_3(6x)

We take antilogarithm to obtain:


(4x+2)=(6x)


2=6x-4x

Simplify


2=2x

Divide both sides by 2


1=x

17. Given
\log_2(3x+12)=4.

We rewrite in exponential form:


(3x+12)=2^4


(3x+12)=16


3x=16-12


3x=4

Divide both sides by 3


x=(4)/(3)

18. Given
\log_3(3x+7)=\log_3(10x)

We take antilogarithm to get:


(3x+7)=(10x)

Group similar terms:


7=10x-3x


7=7x

We divide both sides by 7


x=1

19. Given:
\log_2x+\log_2(x-3)=2

Apply the product rule to simplify the left hand side


\log_2x(x-3)=2

We take antilogarithm to obtain:


x(x-3)=2^2


x^2-3x=4


x^2-3x-4=0


(x-4)(x+1)=0

x=-1 or x=4

But x>0, therefore x=4

20. Given
\ln x+ \ln (x+4)=3

Apply product rule to the LHS


\ln x(x+4)=3

Rewrite in the exponential form to get:


x(x+4)=e^3


x^2+4x=e^3


x^2+4x-e^3=0

This implies that:


x=-6.91 or
x=2.91

User Orujimaru
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories