Mathematical Logarithms and Equations

This set of flashcards covers key concepts and equations related to logarithms and algebraic manipulations as discussed in the lecture notes.

log (x) = 3

The logarithm of x base 10 equals 3; this means x = 10^3 or x = 1000.

5³ = x

This indicates that x equals 5 raised to the power of 3, which is 125.

(3x-8) = -1

An equation where 3 times x minus 8 equals negative 1.

logy (3x-8)= 2

The logarithm of (3x-8) equals 2; this implies 3x-8 = 10^2 or 3x-8 = 100.

If 16=3x-8, then x = 8

This is an equation solved to find that x equals 8.

25=x+9

An equation suggesting that x equals 25 minus 9, leading to x = 16.

log (P+7) = 3, P+3 = 1

If the logarithm of (P+7) equals 3, then it's resolved to find the value of P.

(x-4)(x+4) = 0

A quadratic equation formed by factoring, leading to roots x = 4 and x = -4.

t log b = logz

An equation relating t and b through logarithms, used in exponential equations.

(4m) = log 2 + log (m-3)

Equates a multiple of m to the sum of two logarithms, allowing for the determination of m.