243^0.2x=81^x+5Could you please help me with the steps to this problem?
1 answer:
Answer:
-20/3
Step-by-step explanation:
First simplify the left side of the equation
243^(1/5x)= (243^1/5)^x
=( )^x
= 3^x
Now that the left side is simplified, let's move to the right side
81^(x+5)=( )^(x+5) simplify 81 to base 3^4
= use the product of powers property to multiply the exponents together
=
With both sides simplified, let's rewrite the equation, this time in simplified terms
=
x=4x+20 because both the bases are same, their exponential value must also be equal
-3x=20 solve the algebraic equation for x
x=
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Answer: Domain =
Range =
Step-by-step explanation:
Here, the given function,
Since log( negative number ) = not defined
Also,
Hence, f(x) is defined if x - 1 > 0
⇒ x > 1
Thus, f(x) is defined for all the values that are greater than 1,
⇒ Domain of f(x) = All real number greater than 1,
=
Now, for the interval ,
f(x) can be any real number.
Thus, the range of the given function =