If 2log(x+4)-4log2=1+logx then find the value of x?

1 Answer
Jim G.
Feb 23, 2018

#x=76+-24sqrt10#

Explanation:

#"using the "color(blue)"laws of logarithms"#

#•color(white)(x)logx+logyhArrlog(xy)#

#•color(white)(x)logx-logyhArrlog(x/y)#

#•color(white)(x)logx^nhArrnlogx#

#["note that "log_(10)10=1rArr1=log10]#

#rArrlog(x+4)^2-log2^4=log10+logx#

#rArrlog((x+4)^2/16)=log(10x)#

#rArr(x+4)^2/16=10x#

#rArr(x+4)^2=160x#

#rArrx^2+8x+16=160x#

#"rearrange and equate to zero"#

#rArrx^2-152x+16=0larrcolor(blue)"in standard form"#

#"with "a=1,b=-152" and "c=16#

#"solve for x using the "color(blue)"quadratic formula"#

#x=(152+-sqrt((-152)^2-64))/2#

#color(white)(x)=(152+-sqrt23040)/2=(152+-48sqrt10)/2#

#rArrx=76+-24sqrt10#

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