# Evaluate logarithms Calculator

## Get detailed solutions to your math problems with our Evaluate logarithms 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 Logarithmic differentiation

$\lim_{x\to0}\left(\frac{5^x-1}{\ln\left(1+x\right)}\right)$
2

As the limit results in indeterminate form, we can apply L'Hôpital's rule

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(5^x-1\right)}{\frac{d}{dx}\left(\ln\left(1+x\right)\right)}\right)$
3

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(5^x-1\right)}{\frac{1}{1+x}\cdot\frac{d}{dx}\left(1+x\right)}\right)$
4

The derivative of a sum of two functions is the sum of the derivatives of each function

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(5^x\right)+\frac{d}{dx}\left(-1\right)}{\frac{1}{1+x}\left(\frac{d}{dx}\left(1\right)+\frac{d}{dx}\left(x\right)\right)}\right)$
5

The derivative of the constant function is equal to zero

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(5^x\right)+0}{\frac{1}{1+x}\cdot\frac{d}{dx}\left(x\right)}\right)$
6

The derivative of the linear function is equal to $1$

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(5^x\right)}{\frac{1}{1+x}}\right)$
7

Applying the derivative of the exponential function

$\lim_{x\to0}\left(\frac{\sqrt[4]{45}5^x\frac{d}{dx}\left(x\right)}{\frac{1}{1+x}}\right)$
8

The derivative of the linear function is equal to $1$

$\lim_{x\to0}\left(\frac{\sqrt[4]{45}5^x}{\frac{1}{1+x}}\right)$
9

Simplifying the fraction

$\lim_{x\to0}\left(\sqrt[4]{45}5^x\left(1+x\right)\right)$
10

Solve the product $\sqrt[4]{45}5^x\left(1+x\right)$

$\lim_{x\to0}\left(5^x\left(\sqrt[4]{45}+\sqrt[4]{45}x\right)\right)$
11

Multiplying polynomials $5^x$ and $\sqrt[4]{45}+\sqrt[4]{45}x$

$\lim_{x\to0}\left(\sqrt[4]{45}5^x+\sqrt[4]{45}5^x\cdot x\right)$
12

The limit of a sum of two functions is equal to the sum of the limits of each function: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$

$\lim_{x\to0}\left(\sqrt[4]{45}5^x\right)+\lim_{x\to0}\left(\sqrt[4]{45}5^x\cdot x\right)$
13

Evaluating the limit when $x$ tends to $0$

$5^0\sqrt[4]{45}+\lim_{x\to0}\left(\sqrt[4]{45}5^x\cdot x\right)$
14

Simplifying

$\sqrt[4]{45}+\lim_{x\to0}\left(\sqrt[4]{45}5^x\cdot x\right)$
15

Evaluating the limit when $x$ tends to $0$

$\sqrt[4]{45}+5^0\sqrt[4]{45}0$
16

Simplifying

$\sqrt[4]{45}+0$
17

Add the values $\sqrt[4]{45}$ and $0$

$\sqrt[4]{45}$

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