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Solution for log4(x^4)-2log4(x^2)/4log4(y) equation:
ctg(3*x-6)
(x^8-2)^3
7/12 = 14
(1-x-y)^3
-x
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Precalculus Examples
Solve for x log base 4 of x+ log base 4 of x-12=3
Step 1
Use the product property of logarithms, .
Apply the distributive property.
Step 2
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 3
Rewrite the equation as .
Subtract from both sides of the equation.
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Add to both sides of the equation.
Set equal to and solve for .
Subtract from both sides of the equation.
The final solution is all the values that make true.
Step 4
Exclude the solutions that do not make true.
Algebra Examples
Solve for x log base 4 of x-8+ log base 4 of x-8=1
Use the product property of logarithms, .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Rewrite the equation as .
Subtract from both sides of the equation.
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
Add to both sides of the equation.
Set equal to and solve for .
Add to both sides of the equation.
The final solution is all the values that make true.
Exclude the solutions that do not make true.
see below
lots of ways to do this
#4^(log_4(x+8))=4^2#
you can see immediately that #x+8 = 4^2 implies x = 8#
this is because: #a ^ {ln_a Q} = Q#
or you can plod through mechanically. So, just equating the exponents....
#log_color{red}{4}(x+8)=2 qquad star#
#(x+8)=color{red}{4}^2# same result
or changing the base on the LHS of #star# to 2
#log_color{red}{4}(x+8) = (log_2(x+8))/(log_2 4)#
so
#(log_2(x+8))/(log_2 4)=2#
#implies log_2(x+8)=2* log_2 4#
#implies log_2(x+8)=2* 2 = 4#
#implies (x+8)=2^4 = 16 implies x = 8#