What is expand log_{7}(\sqrt[3]{3^5}) ?

The solution to expand log_{7}(\sqrt[3]{3^5}) is 5/3 log_{7}(3)

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expand log_{7}(\sqrt[3]{3^5})

expand

\frac{5}{3} lo g_{7} (3)

Decimal Notation

0.94095 \dots

Solution steps

Rewrite as

= lo g_{7} ((3^{5})^{\frac{1}{3}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{3} lo g_{7} (3^{5})

Simplify

lo g_{7} (3^{5}) : 5 lo g_{7} (3)

= 5 \cdot \frac{1}{3} lo g_{7} (3)

Multiply fractions:

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

= \frac{1 \cdot 5}{3} lo g_{7} (3)

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{3} lo g_{7} (3)

- 5 (4 + 2)

(2 + x i)^{2}

(a + bi)^{6}

(1 + cos (t)) (e^{t^{2}} + t)^{2}

(x^{2})^{2}

What is expand log_{7}(\sqrt[3]{3^5}) ?
The solution to expand log_{7}(\sqrt[3]{3^5}) is 5/3 log_{7}(3)