Please help! Step by step?? 1. 5^x = 4^x+3

and

2. .16^4+3x = .3^8-x

how do i solve these? step by step please?

the answers are supposed to be:

1. 3log4 / log 1.25

2. (log .3^8 / .16^4 ) / (log (.16^3 x .3)

help?

Question

Please help! Step by step??    1. 5^x  = 4^x+3

and 

2.        .16^4+3x = .3^8-x 


how do i solve these? step by step please? 

the answers are supposed to be: 

1.  3log4 / log 1.25

2.  (log .3^8 / .16^4 ) / (log (.16^3 x .3)

help?

phi · Answer

as a first step I would use the rule

$$ \log( a^b) = b \log(a) $$
take the log of both sides of the equation, and then use that rule.  what do you get?

anonymous · Answer

X log 5 = X+3 log 4

phi · Answer

yes but put parens around the x+3 like this
x log 5 = (x+3) log4

remember that log4 is just a number  (use a calculator to find it... if you are curious what number).  like any number, you can "distribute" it  which means multiply it times everything inside the parens.  

you get
x log 5 =  x log 4 + 3 log 4
subtract x log 4 from both sides:
x log 5 - x log 4 = x log 4 - x log 4 + 3 log 4
of course   x log 4 - x log 4= 0  so this is the same as
x log 5 - x log 4= 3 log 4

factor x out of each term on the left side:
x (log 5 - log 4) = 3 log4

can you finish ?