Answer:
x = 2 and x = 4
Step-by-step explanation:
correct on edg, BUT IF YOU DON'T BELIEVE ME..... please, read below.
log6(x2+8)=1+log6(x)
Move all the terms containing a logarithm to the left side of the equation.
log6(x2+8)−log6(x)=1
Use the quotient property of logarithms, logb(x)−logb(y)=logb(xy)
log6(x2+8x)=1
Rewrite log6(x2+8x)=1
in exponential form using the definition of a logarithm. If x and b are positive real numbers and b≠1, then logb(x)=y is equivalent to by=x
61=x2+8x
Solve for x
Evaluate the exponent.
6=x2+8x
Rewrite the equation as x2+8x=61
x2+8x=6
Evaluate the exponent.
x2+8x=6
Solve for x
Multiply each term by x
and simplify.
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x2+8=6x
Subtract 6x
from both sides of the equation.
x2+8−6x=0
Factor x2+8−6x
using the AC method.
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(x−4)(x−2)=0
Set x−4
equal to 0 and solve for x
x=4
Set x−2
equal to 0 and solve for x
x=2
The solution is the result of x−4=0
and x−2=0
x=4,2
