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5^x=62 Giving 20 points!

Algebra 2, Chapter 6-7. Common Logarithms.
The answer key says its 2.5, but I need some help to understand how to get that answer by showing work.

Respuesta :

Answer:

x = 2.564 ( to 3 dec. places )

Step-by-step explanation:

Using the rule of logarithms

log[tex]x^{n}[/tex] ⇔ n logx

Given

[tex]5^{x}[/tex] = 62 ( take the ln of both sides )

ln[tex]5^{x}[/tex] = ln 62, that is

x ln5 = ln 62 ( divide both sides by ln 5 )

x = [tex]\frac{ln62}{ln5}[/tex] ≈ 2.564

jb417902

Answer:

2.5

Step-by-step explanation:

ln(5^x)=ln(62)

[tex]x=\frac{ln62}{ln5}[/tex]

≈2.56433

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