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Solve the equation. Write the solution set with exact values given in terms of common or natural logarithms.

Solve The Equation Write The Solution Set With Exact Values Given In Terms Of Common Or Natural Logarithms class=

Sagot :

We have to solve for y:

[tex]\begin{gathered} 1282=23^y+2 \\ 23^y=1282-2 \\ 23^y=1280 \\ \log_{23}(23^y)=\log_{23}(1280) \\ y=\log_{23}(1280) \end{gathered}[/tex]

We can express the solution in terms of a logarithm with base 23 as y = log₂₃(1280).

The approximated value is:

[tex]y=\log_{23}(1280)\approx2.2818[/tex]

Answer:

Exact solution: y = log₂₃(1280)

Approximate solution: y ≈ 2.2818

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