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Equations with cubic roots Calculator

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1

Solved example of equations with cubic roots

$\left(8^{\left(x-1\right)}\right)^{\frac{1}{5}}=\left(4^{\frac{1}{3}}\right)^{\left(x+3\right)}$
2

Calculate the power $\sqrt[3]{4}$

$\sqrt[5]{8^{\left(x-1\right)}}=1.5874^{\left(x+3\right)}$
3

Applying the power of a power property

$8^{0.2\left(x-1\right)}=1.5874^{\left(x+3\right)}$
4

Removing the variable from the exponent

$\ln\left(8^{0.2\left(x-1\right)}\right)=\ln\left(1.5874^{\left(x+3\right)}\right)$
5

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$0.2\ln\left(8\right)\left(x-1\right)=\ln\left(1.5874^{\left(x+3\right)}\right)$
6

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$0.2\ln\left(8\right)\left(x-1\right)=\ln\left(1.5874\right)\left(x+3\right)$
7

Calculating the natural logarithm of $1.5874$

$0.2\cdot 2.0794\left(x-1\right)=0.4621\left(x+3\right)$
8

Multiply $0.2$ times $2.0794$

$0.4159\left(x-1\right)=0.4621\left(x+3\right)$
9

Solve the product $0.4621\left(x+3\right)$

$0.4159x+0.4159-1=0.4621x+0.4621\cdot 3$
10

Multiply $0.4621$ times $3$

$0.4159x-0.4159=0.4621x+1.3863$
11

Grouping terms

$0.4159x-0.4159-0.4621x=1.3863$
12

Adding $0.4159x$ and $-0.4621x$

$-0.0462x-0.4159=1.3863$
13

Subtract $-0.4159$ from both sides of the equation

$-0.0462x=1.3863+0.4159$
14

Add the values $1.3863$ and $0.4159$

$-0.0462x=1.8022$
15

Divide both sides of the equation by $-0.0462$

$x=\frac{1.8022}{-0.0462}$
16

Divide $1.8022$ by $-0.0462$

$x=-39$

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