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Solve. Write your answer as an integer or a fraction in simplest form. $\newline$ $4 = 8^x$ $\newline$ $x=$ ______

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Solve exponential equations by rewriting the base

Full solution

Q. Solve. Write your answer as an integer or a fraction in simplest form.

\newline

4 = 8^x

\newline

x=

______

Write as powers of $\newline$ $2$ : Write $\newline$ $4$ and $\newline$ $8$ as powers of $\newline$ $2$ to have a common base. $\newline$ $\newline$ $4$ can be written as $\newline$ $2^2$ and $\newline$ $8$ can be written as $\newline$ $2^3$ . $\newline$ So, $\newline$ $4 = 2^2$ and $\newline$ $8 = 2^3$ .
Rewrite using new expressions: Rewrite the equation using the new expressions for $4$ and $8$ . The original equation $4 = 8^x$ can now be written as $(2^2) = (2^3)^x$ .
Apply power of a power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^b)^c = a^{(b*c)}$ . Therefore, $(2^3)^x = 2^{(3*x)}$ .
Set exponents equal: Set the exponents equal to each other since the bases are now the same. $\newline$ $2^2 = 2^{3x}$ implies that $2 = 3x$ .
Solve for x: Solve for x. $\newline$ Divide both sides of the equation by $3$ to isolate x. $\newline$ $x = \frac{2}{3}$ .

More problems from Solve exponential equations by rewriting the base

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x

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Steven opened a savings account and deposited

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\newline

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A

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Use the following function rule to find

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

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Posted 8 months ago

Question

x

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Posted 4 months ago

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Solve. Round your answer to the nearest thousandth.

\newline

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\newline

x =

Posted 7 months ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

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Posted 9 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

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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

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g(t)

3

\newline

g(t)

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\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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