SOLUTION: If 10^x+10^-x=4. Prove that log base 10( 2+(3^1/2))= x
Algebra.Com
Question 976054: If 10^x+10^-x=4. Prove that log base 10( 2+(3^1/2))= x
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Use the fact that 10^log10(x) = x, and substitute the given value for x:
Does 10^log10(2+sqrt(3)) + 1/10^log10(2+sqrt(3)) = 4 ?
Simplify the LHS:
2+sqrt(3) + 1/(2+sqrt(3)) = ((2+sqrt(3)(2+sqrt(3)) + 1)/(2+sqrt(3))
(4 + 4sqrt(3) + 3 + 1)/(2+sqrt(3)) -> (8+4sqrt(3))/(2+sqrt(3)) = 4(2+sqrt(3))/(2+sqrt(3)) = 4
Done
RELATED QUESTIONS
log base 10(x+4)=2+log base 10 x-log base 10... (answered by josgarithmetic,greenestamps)
log base 10(1-x)=-1
log base 10 (-x-4)=... (answered by stanbon)
Condense the expression. 3log(base 10)2-log(base 10)y+1/3log(base... (answered by fractalier)
Write in terms of the NATURAL LOG. (ln)
1. log (base 4)x
2. log (base 10) (x+1)
3. log (answered by solver91311,jsmallt9)
Log (3x-1) base 5 all over 1 + log x base 5 = 3+log 2 base... (answered by MathLover1)
Solve: 2 * Log base 4(x) + 3 * log base 8(x) =... (answered by jrfrunner)
Solve for x:
(A.) (5/2) log(base 4)4 = log(base 4)(2x-3)
(B.) Log(base 3)(x+2)-... (answered by stanbon)
If p = (50y^2)^3/81x^3 then prove that log10^p + 3 log 10^x - 6 log 10^y
=6-3log10^2... (answered by greenestamps,Alan3354)
solve for x
log(base 10)X+log(base 10)(X+1) = log(base... (answered by nerdybill)