Sunday

December 21, 2014

December 21, 2014

Posted by **anonymous** on Tuesday, January 8, 2013 at 6:30am.

log2(x+4)-log4x=2

please show work

- math -
**Reiny**, Tuesday, January 8, 2013 at 8:46amwe should have the same base in the logs

let log_{4}x = y

then 4^y = x

2^(2y) = x

log_{2}x = 2y

y = (1/2)log_{2}x

= log_{2}x^(1/2)

= log_{2}√x

then log_{4}x = log_{2}√x

log_{2}[ (x+4)/√x] = 2

(x+4)/√x = 2^2 = 4

x+4 = 4√x

square both sides

x^2 + 8x + 16 = 16x

x^2 - 8x + 16 = 0

(x-4)^2 = 0

x-4 = 0

x = 4

**Answer this Question**

**Related Questions**

math - solve the equation log2(x+4)-log4x=2 the 2 and 4 are lower than the g ...

Math - I am having trouble figuring out how to solve these logarithms. Could ...

Math - I am having trouble figuring out how to solve these logarithms. Could ...

Math-Advanced Functions - I am having trouble figuring out how to solve this ...

Math - Logarithmic - Solve: 2^(5x-6) = 7 My work: log^(5x-6) = log7 5x - 6(log2...

Algebra 2 - solve log2(3x-1)-log2(x-1)=log2(x+1) i have absolutely no idea how ...

math/algebra - solve the equation log2(3x-2) - log2 (x-5)=4

Algebra II - Please check answers: Use the equation of the exponential function ...

Algebra II - Solve log2(7x-3)>= log2(x+12) My work: 6x=15 x=15/6 x-5/2 so my ...

Math Algebra 2 - How do I put log in a TI-84 calculator. #1.Express the ...