SOLUTION: How do I solve these problems? 1. log(2 - x) = 0.5 2. log(x + 25) = log(x + 10) + log 4

Question 965036: How do I solve these problems?
1. log(2 - x) = 0.5
2. log(x + 25) = log(x + 10) + log 4

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the first one is solved as follows:

log(2-x) = .5

this is true if and only 10^.5 = 2-x

square both sides of this equation to get:

10 = (2-x)^2

simplify to get:

10 = 4 - 4x + x^2

subtract 10 from both sides and re-arrange the terms to get:

x^2 - 4x - 6 = 0

factor using the quadratic formula to get:

x = 5.16227766

x = -1.16227766

both values work.

just replace them in the original equation and you'll see.

the second problem is solved as follows:

log(x + 25) = log(x + 10) + log 4

this is equivalent to log(x + 25) = log(4 * (x + 10) which is equivalent to log(x + 25) = log(4x + 40).

this is true if and only if x + 25 = 4x + 40

solve for x to get x = -5.

replace x with -5 in the original equation and you'll see that they're equivalent.

log(-5 + 25) = log(20).\

log(x + 10) + log(4) is equal to log(5) + log(4) which is equal to log(5 * 4) which is equal to log(20).

the rule of logs that are used are:

logb(x) = y if and only if b^y = x

logb(a) + logb(b) = logb(a * b)

RELATED QUESTIONS
log 2 + log x = log 3 log 2 + log x = 3 I'm so confused, how do I solve these?... (answered by rapaljer)

How do i write these as a single logarithm? 1) (log 3 - log 4) - log 2 2) log 2 +... (answered by Boreal)

How do I solve this simultaneous logarithm. log (x-4)+ 2 log y = log 16 log x + log y = (answered by stanbon)

How do I solve log x + log 2 =... (answered by stanbon)

How do I work log(x-1)-log(x+6)=log(x-2)-log(x+3) (answered by josgarithmetic)

I need help solving these problems. {{{ 2log(3,x)-log(3,x-4)=(2)+log(3,2)}}} and (answered by josmiceli,lwsshak3)

How can in solve it ?!=(... (answered by jsmallt9)

how do you solve log base 4 (log base 3 (log base 2 of X)) = 0?? (answered by stanbon)

Solve for x. a.) log sub2(log sub4{log sub3[log sub2 x]}) = -1 b.) log sub2(x+4)... (answered by MathLover1)