Solve the following equation??

Question

solve 20^x = 3 (4^x) in the form of logarithm, giving ur ans correct to 3 significant figures

Include the steps as well

Ok, just to make it more clear,

solve 20^x = 3 (4^x) in the form of logarithm, giving your answer correct to 3 significant figures

Include the steps as well

Answer 1

20^x = 3 (4^x)
log [20^x] = log[3 (4^x)]
xlog20 = log3 + xlog4

xlog20 - xlog4 = log 3
x(log20 -log4) = log 3

x = log3 / (log20 - log4) = .4771 / (1.3010 - .6021) = 0.683

check:
20^.683 = 3 (4^.683)
7.738 = 3 (2.578)
7.738 = 7.734 (approximately)

Answer 2

You start by splitting the 20 into 5 x 4. This will make the 4s cancel out. You will then need to take logs of both sides.

Answer 3

By factorizing, we can write:

20^x = 3 (4^x) as:

(5^x)*(4^x) = 3(4^x). Dividing both sides by non-zero common factor 4^x:

5^x = 3. And now taking logarithms on both sides:

x*ln(5) = ln(3), giving:

x = ln(3)/ln(5)

= 1.0986/1.609

= 0.683 (approximately)

Answer 4

20^x = 3 (4^x);
4^x * 5^x = 3 * 4^x;
5^x = 3;
x log 5 = log 3;
x = log 3 / log 5.

log(3) / log(5) = 0.682606194

x = 0.683

Answer 5

Take logs of both sides
xln(20) = ln(3) + xln(4) then do a bit of 7'th grade algebra
x = ln(3)/(ln(20) - ln(4))

Now go punch numbers into your calculator. ☺


Doug

Answer 6

(5 x 4)^(x) = 3(4^x)

(5^x ) x 4^(x) = 3(4^x)

5^(x) = 3

x log 5 = log 3

x = log 3 / log 5

x = 0.683

Answer 7

Please restate the question in English if you want to be both understood and taken seriously (what's an 'ur ans'?).