Solve this equation~~?

Question

Find the value of x.

4^(2x) /8^(x) = 16^(x + 1) / 3^(2x)

Thanks.....

Answer 1

apply log
xlog8/xlog8=(x+1)log16/xlog9

1=(x+1)log16/xlog9
xlog9=xlog16+log16
x(log9-log16)=log16 => x=log16/log9-log16 => x=- 0,25

Answer 2

4^2x / 8^x = 16^(x + 1)/3^2x

Change 4,8 and 16 to a power of 2
2^4x / 2^3x = 2^(4x + 4)/3^2x

We "shift" 3^2x to the left by cross-multiplying and "shift" the powers of 2 to the right side
3^2x = 2^(4x + 4) · 2^3x / 2^4x

Using exponent properties,
3^2x = 2^(4x + 4 + 3x - 4x)

Thus,
3^2x = 2^(3x + 4)

Get the ln of both sides:
ln 3^2x = ln 2^(3x + 4)

Thus,
2x ln 3 = (3x + 4) ln 2

Distribute ln 2
2x ln 3 = 3x ln 2 + 4 ln 2

Thus,
2x ln 3 - 3x ln 2 = 4 ln 2

Factor x
x (2 ln 3 - 3 ln 2) = 4 ln 2

and
x = 4 ln 2/(2 ln 3 - 3 ln 2)

We combine the ln's into one ln (logarithm)
x = ln 2^4/(ln 3^2 - ln 2^3)
x = ln 16/(ln 9/8)
x = log_9/8 16 or
x = 4 log_9/8 2

The answer is:
x = 4 times the logarithm of 2 to the base 9/8.
or approximately 23.5398. Try substituting. You will get a good result!

Try
^_^

Answer 3

x= 8/5

Answer 4

Simplify 4^(2x)/8^(x) = 2^(4x)/2^(3x) = 2^x. Then
(2^x)*(3^2x) = 16^(x+1) and
x*log2 + 2x*log3 = (x+1)*log16

Now crank up the calculator and solve it for x ☺


Doug

Answer 5

x = (4ln2) / ln(9/8) <--- that's the answer.

Try to express 4, 8 and 16 as a power of 2.
Then, use the PROPERTIES of LN ( natural logarithms) in order to solve for x. please check it out.

Answer 6

the previous guy's answer is correct. x=8/5

Answer 7

x=ln(16)/(ln9-ln 8)

Answer 8

2xln4-xln8=xln16+ln16-2xln3
x(2ln4-ln8-ln16+2ln3)=ln16
x(ln16-ln8-ln16+ln9)=ln16
xln(9/8)=ln16
x=ln16/ln(9/8)
x=23.54