Question

5,1^1/2(х-3)=5,1корень 5,1 решить показательное уравнение

Answer 1

$5,1^{ \frac{1}{2} (x-3)}=5,1 \sqrt{5,1} \\5,1^{ \frac{1}{2} (x-3)}=5,1 ^{ \frac{3}{2}} \\ \frac{1}{2} (x-3)}=\frac{3}{2}$
x-3=3
x=6

Answer 2

I can help you solve the exponential equation. Here is the detailed solution:

- First, we need to rewrite the equation in the form of $$a^x=b$$, where $$a$$ and $$b$$ are constants and $$x$$ is the unknown variable. - To do this, we can use the property that $$a^{mn}=(a^m)^n$$, which means that we can raise both sides of the equation to the power of $$2$$ and get rid of the square roots. - We get $$\left(5.1^{1/2(x-3)}\right)^2=\left(5.1\sqrt{5.1}\right)^2$$, which simplifies to $$5.1^{x-3}=5.1^2\cdot 5.1=5.1^3$$. - Now we have the equation in the desired form, with $$a=5.1$$ and $$b=5.1^3$$. - To solve for $$x$$, we can use the property that $$a^x=b \iff x=\log_a b$$, which means that we can take the logarithm of both sides with base $$a$$ and get the value of $$x$$. - We get $$x=\log_{5.1} 5.1^3$$, which simplifies to $$x=3\log_{5.1} 5.1$$. - Using the property that $$\log_a a=1$$, we can further simplify the expression to $$x=3$$. - Therefore, the solution of the exponential equation is $$x=3$$.

You can also use the online calculators from the web search results to check your answer or to solve other exponential equations. For example, you can try [this one](https://www.math-solution.ru/math-task/exponential-equality) or [this one](https://ru.symbolab.com/solver/equation-calculator). I hope this helps.