Math problem: 18^(-10x)=13^(x-3)?

Question

I was told to use base 10 log. I'm not sure what to do with the "18" and "13" though. Please help! :(

Answer 1

To base e

18^(-10x)=13^(x-3)

-10x*ln(18)=(x-3)*ln(13)

-10x*ln(18)=x*ln(13)-3*ln(13)

3*ln(13)=x*(ln(13)+10*ln(18))

x=(3*ln(13)/(ln (13)+10*ln(18))=0.2445

Answer 2

its obviously 432>4324=(54x)42

DUH

Answer 3

milk.

Answer 4

18^(-10x) = 13^(x-3)

-10x.log(18) = (x-3)log(13)

-10x.log(18) = x.log(13) - 3log(13)

x(log(13) + 10log(18)) = 3log(13)

x = 3log(13) / [(log(13) + 10log(18))]

x ≈ 0.24452

Answer 5

Take the log of each side:

(-10x)*log18 = (x-3)*log13

which simplifies to

3log13 = x(log13+10log18) or

x = (3log13)/(log13+10log18) = .2445

BTW, the answer is the same no matter what base you use for your logarithms.  

Answer 6

18^( -10x ) = 13^( x - 3)

Take the log of both sides.

log ( 18^( -10x ) ) = log ( 13^( x - 3 ) )

Use the power property of logarithms.

-10x log (18 ) = (x - 3) log (13 )

Distribute

-10x log ( 18 ) = x log ( 13 ) - 3 log ( 13 )

-10x log ( 18 ) - x log ( 13 ) = -3 log ( 13 )

Factor out the x

x ( -10 log ( 18 ) - log ( 13 ) ) = -3 log ( 13 )

x = [ -3 log ( 13 ) ] / [ -10 log ( 18 ) - log ( 13 ) ]

x ≈ 0.2445241194