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Radical equations and functions Calculator

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1

Solved example of Radical equations and functions

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

Multiply $4$ times $\sqrt{2}$

$\left(\sqrt{2}\right)^{\left(x-3\right)}=\left(\sqrt{47}\right)^{\left(x+1\right)}$
3

Removing the variable from the exponent

$\ln\left(\left(\sqrt{2}\right)^{\left(x-3\right)}\right)=\ln\left(\left(\sqrt{47}\right)^{\left(x+1\right)}\right)$
4

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

$\ln\left(\sqrt{2}\right)\left(x-3\right)=\ln\left(\left(\sqrt{47}\right)^{\left(x+1\right)}\right)$
5

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

$\ln\left(\sqrt{2}\right)\left(x-3\right)=\ln\left(\sqrt{47}\right)\left(x+1\right)$
6

Calculating the natural logarithm of $\sqrt{47}$

$\frac{7}{\sqrt[3]{3}}\left(x-3\right)=\sqrt[3]{14}\left(x+1\right)$
7

Solve the product $\sqrt[3]{14}\left(x+1\right)$

$\frac{7}{\sqrt[3]{3}}x-\sqrt[3]{7}=\sqrt[3]{14}x+\sqrt[3]{14}$
8

Grouping terms

$\frac{7}{\sqrt[3]{3}}x-\sqrt[3]{7}-\sqrt[3]{14}x=\sqrt[3]{14}$
9

Adding $\frac{7}{\sqrt[3]{3}}x$ and $-\sqrt[3]{14}x$

$-\sqrt[3]{7}-\frac{17}{\sqrt{3}}x=\sqrt[3]{14}$
10

Subtract $-\sqrt[3]{7}$ from both sides of the equation

$-\frac{17}{\sqrt{3}}x=3.5835$
11

Multiply both sides of the equation by $-\frac{2}{\sqrt{2}}$

$x=-2.585$