Logs: maths exam question thats bugging me... 2^(x+3) = 3^(x+2)... use logs to find x...anyone help? :)?

Question

btw... ^ means "to the power of"

Answer 1

takin log on both sides
(x+3) log2=(x+2)log3
x(log2-log3)= log9 - log8
x(log2/3)=log(9/8)
x=log(9/8) /(log2/3) or log9-log8/(log2-log3)
use the values of log & get d ans.

Answer 2

Addition of two logarithms could be rewritten as multiplication like so: log[ (3x - a million) * (2x+3) ] = log (4x) log( 6x^2 + 7x - 3 ) = log(4x) The words interior the logarithms must be equivalent if the logarithms themselves are equivalent, so: 6x^2 + 7x - 3 = 4x 6x^2 + 3x - 3 = 0 3(x^2 + x - a million) = 0 x^2 + x - a million = 0 x = (-a million +/- sqrt(a million+4))/2 [quadratic formulation, or finished the sq., whichever] x = (-a million +sqrt(5))/2 [We dismiss the adverse answer, while you evaluate that could make 4x adverse, and you may not take the logarithm of adverse numbers. desire that facilitates!

Answer 3

2^(x+3) = 3^(x+2)... (take log to base 10 - or any base).
log [2^(x+3)] = log [3^(x+2)] (by rules of logs).
(x+3)log 2 = (x+2)log 3
(x+3)(0∙301 029 995...) = (x+2)(0∙477 121 254...)
0∙301 029 995...x + 0∙903 089 987 = 0∙477 121 254...x + 0∙954 242 504
- 0∙0511 525 17 = 0∙176 091259 ....x
-0∙290 488 677 = x

Answer 4

Take log to the base 10 on both the sides...

use the property log(a^b) = b * log(a)

you will get (x+3)*log2 = (x+2)* log3

because you know "a" in ur problem,you will get a linear equation... solve it...

Answer 5

2^(x + 3) = 3^(x + 2)

Take log of both sides:
log[2^(x + 3)] = log[3^(x + 2)]
(x + 3)log(2) = (x + 2)log(3)

Expand:
xlog(2) + 3log(2) = xlog(3) + 2log(3)

Rearrange by putting terms in x on the LHS:
xlog(3) - xlog(2) = 3log(2) - 2log(3)

LHS is:
x[log(3) - log(2)] = xlog(3/2)

RHS is:
log(2^3) - log(3^2) = log(8) - log(9) = log(8/9)

So, xlog(3/2) = log(8/9)

Thus, x = log(8/9) / log(3/2) as the exact answer.

Answer 6

Hi

2^(x+3)=3^(x+2)
log(2^(x+3))=log(3^(x+2))
(x+3)*log(2)=(x+2)*log(3)
(x+3)/(x+2)=log3/log2=1.58
x=-0.29

good luck

Answer 7

(x + 3).log 2 = (x + 2).log3
0.693.(x + 3) = 1.099(x + 2)
0.693.x + 2.079 = 1.099x + 2.198
- 0.119 = 0.406x
x = - 0.293

Answer 8

2^(x+3) = 3^(x+2)
2³(2^x) = 3²(3^x)
8(2^x) = 9(3^x)

ln[8(2^x)] = ln[9(3^x)]
ln8 + xln2 = ln9 + xln3
ln8 - ln9 = xln3 - xln2 = x(ln3 - ln2)
ln(8/9) = x[ln(3/2)]

x = ln(8/9) / ln(3/2) ≈ -0.2904887

Answer 9

Ohhh ain't this about a....

I kinda remember that cuz I took that last year..

Girl I don't know let's just go party cuz I hate Math with a passion.