Question

solve for x using logarithm:
25^x-3(5^x)=0​

Answer 1

Answer:

$x = 0.68$

Step-by-step explanation:

We would like to find out the value of x using logarithms of the given equation .The equation is ,

$\longrightarrow 25^x - 3(5^x)=0$

Add $3(5^x)$ on both sides,

$\longrightarrow 25^x = 3(5^x)$

Using log to the base 10 on both sides, we have;

$\longrightarrow log_{10}(25^x) = log_{10}\{3(5^x)\}$

Recall that $log(ab ) = log\ a + log\ b$ .

$\longrightarrow log_{10}(25^x)=log_{10}3 + log_{10}5^x$

Recall the properties of logarithm as $log\ a^b = b\ log\ a$ .

$\longrightarrow xlog25 = log_{10}3 + xlog_{10}5$

Again we can rewrite it as ,

$\longrightarrow xlog(5^2)=log_{10}3+xlog_{10}5$

$\longrightarrow 2x\ log_{10}5 = log_{10}3+xlog_{10}5$

$\longrightarrow 2x\ log_{10}5-x\ log_{10}5 = log_{10}5$

Simplify,

$\longrightarrow x\ log_{10}5=log_{10}3$

Divide both sides by log5 ,

$\longrightarrow x =\dfrac{log_{10}3}{log_{10}5}$

Put on the values of log 3 and log5 ,

$\longrightarrow x =\dfrac{0.47}{0.69}$

Simplify,

$\longrightarrow \underline{{\underline{\boldsymbol{ x = 0.68}}}}$

And we are done!