can u help me with this math question?

Question

7^ (4x-3) = 31 i know we have to use the laws of ln, but i dont know how. the books examples again didnt help at all. thankds for ur time. Serious anwers only please, if you dont know, then its fine,.. dont bother. but thank you.

Answer 1

Hi Dear;
Step 1;
you need to take ' ln' of both side;
ln[7^(4x-3)] = ln(31)

Step 2;
Here you have to bring the exponent down in front of ln
[(4x-3) ln(7)] = [ln(31)]

Step 3;
[4x ln(7) - 3 ln(7)] = [ln(31)]

Step 4;
So Here you should remove '3 ln(7)' just add '3 ln(7)' to both side
4x ln(7) = ln(31) + 3 ln(7)

Step 5;
Now Divide both sides by '4 ln(7)' so we have ;
x = [ ln(31) + 3 ln(7) ] / (4 ln(7))

Good Luck.

Answer 2

Take the ln of each side
ln(7^(4x-3)) = ln(31)
Now bring the exponent down in front of ln
(4x-3) ln(7) = ln(31)
Distribute on the left side
4x ln(7) - 3 ln(7) = ln(31)
Add 3 ln(7) to each side
4x ln(7) = ln(31) + 3 ln(7)
Divide both sides by 4 ln(7)
x = [ ln(31) + 3 ln(7) ] / (4 ln(7))

Answer 3

The laws of ln allow you to bring the exponent down as a multiplier to the ln of the number:

(4x-3)ln7 = ln31

(4x-3) = ln31/ln7

x = 1/4(ln31/ln7+3)

Answer 4

7^ (4x-3) = 31
(take ln of both sides)
(4x-3)*ln(7) = ln(31)

4x-3 = ln(31)/ln(7)

x = (ln(31)/ln(7) + 3)/4

:D

Answer 5

7 ^ (4x-3) = (7^ 4x)/ (7^3) = ((7^4)^x) / (7^3)
= (2401 ^ x) / 343 = 31 since 7^3 = 343 and
7^4 = 2401

So 2401^x = (31)(343) = 10633

and so log(2401^x) = x log 2401 = log 10633

or x = (log 10633)/(log 2401) = 4.0267 / 3.3804 = 1.1912

Answer 6

yes