For any algebraic expressions
and
and any positive real number
where
if and only if
Definition of a logarithm
For any algebraic expression
S and positive real numbers
and
where
if and only if
One-to-one property for logarithmic functions
For any algebraic expressions
S and
T and any positive real number
where
if and only if
Key concepts
We can solve many exponential equations by using the rules of exponents to rewrite each side as a power with the same base. Then we use the fact that exponential functions are one-to-one to set the exponents equal to one another and solve for the unknown.
When we are given an exponential equation where the bases are explicitly shown as being equal, set the exponents equal to one another and solve for the unknown. See
[link] .
When we are given an exponential equation where the bases are
not explicitly shown as being equal, rewrite each side of the equation as powers of the same base, then set the exponents equal to one another and solve for the unknown. See
[link] ,
[link] , and
[link] .
When an exponential equation cannot be rewritten with a common base, solve by taking the logarithm of each side. See
[link] .
We can solve exponential equations with base
by applying the natural logarithm of both sides because exponential and logarithmic functions are inverses of each other. See
[link] and
[link] .
After solving an exponential equation, check each solution in the original equation to find and eliminate any extraneous solutions. See
[link] .
When given an equation of the form
where
is an algebraic expression, we can use the definition of a logarithm to rewrite the equation as the equivalent exponential equation
and solve for the unknown. See
[link] and
[link] .
We can also use graphing to solve equations with the form
We graph both equations
and
on the same coordinate plane and identify the solution as the
x- value of the intersecting point. See
[link] .
When given an equation of the form
where
and
are algebraic expressions, we can use the one-to-one property of logarithms to solve the equation
for the unknown. See
[link] .
Combining the skills learned in this and previous sections, we can solve equations that model real world situations, whether the unknown is in an exponent or in the argument of a logarithm. See
[link] .
Section exercises
Verbal
How can an exponential equation be solved?
Determine first if the equation can be rewritten so that each side uses the same base. If so, the exponents can be set equal to each other. If the equation cannot be rewritten so that each side uses the same base, then apply the logarithm to each side and use properties of logarithms to solve.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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