S.O.S. Mathematics CyberBoard

A few log problems from a study guide that aren't anything close to what is in the book...

1. 8^3x-1 = 20

2. Given that logz2 = 0.333 and logz5 = 0.774, find logz0.4

3. Use change of base formula to solve 2.5^4x = 100

4. Use change of base formula to evaluate expression, then convert it to a logarithm in base 9: log6973

Any and all help is greatly appreciated.

1st

8^3x=21↔3x=〖Log〗_8 21↔x=(〖Log〗_8 21)/3
2nd

〖Log〗_z 0,4=〖Log〗_z 2/5=〖Log〗_z 2-〖Log〗_z 5=⋯

3rd

〖4x=Log〗_2,5 100↔4x=(〖Log〗_10 100)/(〖Log〗_10 2,5)=⋯
4th
Similar to 3rd

8^3=512, so you get 512x=21, so x=21/512.

Similarly for #3, evaluate 2.5^4 and divide both sides by it to get x.

I'm not seeing why you think you need logs for these, unless you forgot some parentheses.

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