CAIE IGCSE Additional Math 6.3 solve exponential equations

Use this exponential-equations page to take logarithms, collect x terms and round answers only to the accuracy requested.

Exam points

Use logarithms to solve equations with different exponential bases accurately.
Collect terms in x after taking logs or simplifying exponential expressions.
Round answers to one decimal place or three decimal places only when requested.

[Maximum number: 3]

Solve the equation $5^{2y-1}=6\times 3^y$ , giving your answer correct to 3 decimal places.

$(2y-1)\log 5=\log 6+y\log 3$
oe, or $2y\log 5=\log 30+y\log 3$ oe
OR rearranges $\frac{5^{2y}}{5}=6\times3^y$ and collects powers to $\left(\frac{5^2}{3}\right)^y=30$ oe
M1
$y(2\log5-\log3)=\log6+\log5$
oe, or $y(2\log5-\log3)=\log30$ oe
OR $y=\log_{25/3}30$ oe, or $y\log\left(\frac{5^2}{3}\right)=\log30$ oe
M1 FT if of equivalent difficulty
1.604
A1 cao

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6.3. Solve exponential equations question 1