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Solve the following logarithm problem for the positive solution for
x.

log_(x)729=(6)/(5)
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{x} 729=\frac{6}{5}$ $\newline$ Answer:

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Quotient property of logarithms

Full solution

Q. Solve the following logarithm problem for the positive solution for

x

.

\newline

\log _{x} 729=\frac{6}{5}

\newline

Answer:

Understand given logarithmic equation: Understand the given logarithmic equation. $\newline$ We are given the logarithmic equation $\log_{x} 729 = \frac{6}{5}$ . We need to find the value of $x$ that makes this equation true.
Convert to exponential form: Convert the logarithmic equation to its exponential form. $\newline$ The logarithmic equation $\log_{x} 729 = \frac{6}{5}$ can be rewritten in its exponential form as $x^{\frac{6}{5}} = 729$ .
Recognize $729$ as power of $3$ : Recognize that $729$ is a power of $3$ . We know that $729$ is $3$ raised to the power of $6$ because $3^6 = 729$ .
Set exponential equation with base $3$ : Set the exponential equation with the base of $3$ . $\newline$ Since $x^{\frac{6}{5}} = 729$ and $729 = 3^6$ , we can write $x^{\frac{6}{5}} = 3^6$ .
Solve for $x$ by taking $5$ th root: Solve for $x$ by taking the $5$ th root of both sides. $\newline$ To isolate $x$ , we take the $5$ th root of both sides of the equation. This gives us $x = (3^6)^{1/5}$ .
Simplify expression for $x$ : Simplify the expression for $x$ . Using the property of exponents $(a^{m})^{n} = a^{m*n}$ , we simplify $x = (3^{6})^{1/5}$ to $x = 3^{6/5}$ .
Calculate value of x: Calculate the value of $x$ . $\newline$ Since $3^{6/5}$ is the same as $3^{6/5}$ , we find that $x = 3^{6/5} = 3^{1+1/5} = 3 \times 3^{1/5}$ .
Recognize $5$ th root of $3$ : Recognize that $3^{1/5}$ is the $5$ th root of $3$ . $\newline$ The $5$ th root of $3$ is simply $3$ , so $x = 3 \times 3 = 9$ .

More problems from Quotient property of logarithms

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x

\newline

5^x=1

\newline

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Write your answer in simplest form.

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Steven opened a savings account and deposited

\$100.00

as principal. The account earns

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interest, compounded annually. What is the balance after

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\newline

Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

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P

is the principal (starting amount),

r

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Round your answer to the nearest cent.

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Use the following function rule to find

f(1)

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The town of Valley View conducted a census this year, which showed that it has a population of

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\newline

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y = a(b)^x

that can model the town population,

y

x

decades after this census was taken.

\newline

Use whole numbers, decimals, or simplified fractions for the values of

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\newline

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Solve. Simplify your answer.

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Posted 9 months ago

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Solve. Simplify your answer.

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Posted 7 months ago

Question

g(t) = 3^t

change over the interval from

t = 3

t = 4

\newline

\newline

g(t)

3

\newline

g(t)

3

\newline

g(t)

3\%

\newline

g(t)

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Posted 4 months ago

Question

f(x)

6

over every unit interval in

x

f(0) = 0

\newline

Which could be a function rule for

f(x)

\newline

\newline

f(x) = 6x

\newline

f(x) = 6^x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

Posted 4 months ago

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