# Radical equations and functions Calculator

## Get detailed solutions to your math problems with our Radical equations and functions step by step calculator. Sharpen your math skills and learn step by step with our math solver. Check out more online calculators here.

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### Difficult Problems

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 $-\frac{2}{\sqrt{2}}$

$x=-2.585$