Write in log form $$a^b=c$$

Write in power form $$\log_ac=b$$

$$\log_a\left(\frac{b}{c}\right)$$

What is a good strategy for: $$5\times20^x=8\times2^x$$

Remember: $$\frac{20^x}{2^x}=\left(\frac{20}{2}\right)^x=10^x$$

What is a good strategy for: $$\left(\sqrt[3]{2}\right)^x=4^{x-1}$$ (Non-Calculator)

Remember: Change the bases to the same value to then compare powers.

What is a good strategy for: $$5^{x+3}=7$$ (Calculator)

Remember: Write in log form, and use calculator to solve it.

What is a good strategy for: $$7^{x-2}=5^{x+3}$$ Solve this leaving your answer in terms of natural logs. (Non-Calculator)

Remember: Apply ln on both sides, drop the powers in front, expand out, bring all x terms to one side, isolate x by factorising it out.

Logarithms Flashcards

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