What is the answer to log_{x}(8)sqrt(2)= 7/4 ?

The answer to log_{x}(8)sqrt(2)= 7/4 is x=8^{(4sqrt(2))/7}

Solve for x: log_{x}(8)sqrt(2)= 7/4

The solution is x=8^{(4sqrt(2))/7}

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lo g_{x} (8) 2 = \frac{7}{4}

x = 8^{\frac{4 2}{7}}

Decimal

x = 5.36793 \dots

Solution steps

lo g_{x} (8) 2 = \frac{7}{4}

Divide both sides by

2

lo g_{x} (8) = \frac{7 2}{8}

Simplify

\frac{7 2}{8} : \frac{7}{4 2}

lo g_{x} (8) = \frac{7}{4 2}

Apply log rules

\frac{1}{lo g _{8} ( x )} = \frac{7}{4 2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 42 = lo g_{8} (x) \cdot 7

Simplify

42 = lo g_{8} (x) \cdot 7

Switch sides

lo g_{8} (x) \cdot 7 = 42

Divide both sides by

7

lo g_{8} (x) = \frac{4 2}{7}

Apply log rules

x = 8^{\frac{4 2}{7}}

Verify Solutions:

x = 8^{\frac{4 2}{7}}

True

The solution is

x = 8^{\frac{4 2}{7}}

lo g_{10} (x) = 1 - lo g_{10} (30)

ln (x) = 354.08

ln (x) + c

lo g_{10} ((8 x + 1)^{2}) = 2

ln (x - 2) = - 1

What is the answer to log_{x}(8)sqrt(2)= 7/4 ?
The answer to log_{x}(8)sqrt(2)= 7/4 is x=8^{(4sqrt(2))/7}
Solve for x: log_{x}(8)sqrt(2)= 7/4
The solution is x=8^{(4sqrt(2))/7}