\text{Solve for }x of 4^x = 4 \sqrt{3}

x=\frac{4+\log_{2}{\left(3\right)}}{4}

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Question :

4^x = 4 sqrt3

Solve the equation

x = \frac{4 + lo g _{2} ( 3 )}{4}

Alternative Form

x \approx 1.396241

Evaluate

4^{x} = 43

Take the logarithm of both sides

lo g_{4} (4^{x}) = lo g_{4} (43)

Evaluate the logarithm

x = lo g_{4} (43)

Solution

More Steps

Evaluate

lo g_{4} (43)

Use lo g_{a} (x \times y) = lo g_{a} (x) + lo g_{a} (y) to transform the expression

lo g_{4} (4) + lo g_{4} (3)

Use lo g_{a} a^{n} = n to simplify the expression

1 + lo g_{4} (3)

Simplify the expression

More Steps

Evaluate

lo g_{4} (3)

Write the number in exponential form with the base of 3

lo g_{2^{2}} (3^{\frac{1}{2}})

Use lo g_{a^{m}} b^{n} = \frac{n}{m} lo g_{a} b to simplify the expression

\frac{\frac{1}{2}}{2} lo g_{2} (3)

Multiply the terms

\frac{1}{4} lo g_{2} (3)

1 + \frac{1}{4} lo g_{2} (3)

Rewrite the expression

1 + \frac{lo g _{2} ( 3 )}{4}

Reduce fractions to a common denominator

\frac{4}{4} + \frac{lo g _{2} ( 3 )}{4}

Write all numerators above the common denominator

\frac{4 + lo g _{2} ( 3 )}{4}

x = \frac{4 + lo g _{2} ( 3 )}{4}

Alternative Form

x \approx 1.396241

Show Solution

Graph

Frequently Asked Questions

$Solve for x$ of $4^x = 4 \sqrt{3}$

$x = \frac{4 + lo g _{2} ( 3 )}{4}$

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English

4^x = 4 sqrt3

Solve the equation

Graph

Frequently Asked Questions

Solve for x of \(4^x = 4 \sqrt{3}\)

$Solve for x$ of \(4^x = 4 \sqrt{3}\)