For each equation solve one of them by using powers of the same number.to the nearest hundredth, solve the other by using logarithms.
25^x=2

To solve the equation [tex]25^x = 2[/tex] using logarithms, we can take the logarithm of both sides. Specifically, we'll use the natural logarithm (ln) to maintain consistency.

Given:

[tex]25^x = 2[/tex]

Taking the natural logarithm of both sides:

[tex] \ln(25^x) = \ln(2) [/tex]

Using the property of logarithms that [tex] \ln(a^b) = b \cdot \ln(a) [/tex], we get:

[tex] x \cdot \ln(25) = \ln(2) [/tex]

Now, to isolate [tex]x[/tex], we divide both sides by [tex]\ln(25)[/tex]:

[tex] x = \dfrac{\ln(2)}{\ln(25)} [/tex]

Using a calculator:

[tex] x \approx \dfrac{0.6931471806}{3.218875825} [/tex]

[tex] x\approx 0.215338279 [/tex]

[tex] x \approx 0.22 \textsf{(in nearest hundredth)}[/tex]

Therefore, the value of x is 0.22

For each equation solve one of them by using powers of the same number.to the nearest hundredth, solve the other by using logarithms. 25^x=2

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For each equation solve one of them by using powers of the same number.to the nearest hundredth, solve the other by using logarithms.
25^x=2