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Consider the logarithms base 5. For each logarithmic expression below, either calculate the value of the expression or explain why the expression does not make sense.
log5(25)

Respuesta :

boffeemadrid

Answer:

x = 2

Step-by-step explanation:

[tex]log_525=x\\\Rightarrow 5^x=25[/tex]

Taking logarithm to base 10 on both sides we get

[tex]log5^x=log25[/tex]

From logarithm property

[tex]logy^x=xlogy[/tex]

[tex]\Rightarrow xlog5=log25\\\Rightarrow x=\frac{log25}{log5}\\\Rightarrow x=2[/tex]

[tex]\therefore x=2[/tex]

Also we know that

[tex]5\times 5=25\\\Rightarrow 5^2=25[/tex]

Hence, x = 2

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