EXAMPLE 7 Use a logarithmic model M = 5 log D + 2 where D is the diameter (in millimeters) of the telescope’s objective lens. If a telescope can reveal.

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EXAMPLE 7 Use a logarithmic model M = 5 log D + 2 where D is the diameter (in millimeters) of the telescope’s objective lens. If a telescope can reveal stars with a magnitude of 12, what is the diameter of its objective lens? The apparent magnitude of a star is a measure of the brightness of the star as it appears to observers on Earth. The apparent magnitude M of the dimmest star that can be seen with a telescope is given by the function Astronomy

EXAMPLE 7 SOLUTION Use a logarithmic model M = 5 log D = 5 log D = 5 log D 2 = log D 100 = D 10 = 10 2 Log D Write original equation. Substitute 12 for M. Subtract 2 from each side. Divide each side by 5. Exponentiate each side using base 10. Simplify. The diameter is 100 millimeters. ANSWER

GUIDED PRACTICE for Example WHAT IF? Use the information from Example 7 to find the diameter of the objective lens of a telescope that can reveal stars with a magnitude of 7.