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Property 4

Given: log3 m...

Question

Given: $l o g_{3} m = x$ and $l o g_{3} n = y$ .

(i) Express $3^{2 x - 3}$ in terms of m.

(ii) Write down $3^{1 - 2 y + 3 x}$ in terms of m and n.

(iii) If $2 l o g_{3} A = 5 x - 3 y$ ; find A in terms of m and n.

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Solution

(i)

(ii)

$c o n s i d e r space t h e space g i v e n space e q u a t i o n 3 to the power of 1 minus 2 y plus 3 x end exponent equals 3 to the power of 1 cross times 3 to the power of negative 2 y end exponent cross times 3 to the power of 3 x end exponent rightwards double arrow 3 over open parentheses 3 to the power of y close parentheses squared cross times open parentheses 3 to the power of x close parentheses cubed rightwards double arrow 3 over n squared cross times m cubed t h e r e f o r e space 3 to the power of 1 minus 2 y plus 3 x end exponent equals fraction numerator 3 m cubed over denominator n squared end fraction$

(iii)

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Similar questions

State true or false:

{log}_{3} m = x

{log}_{3} n = y

2 {log}_{3} A = 5 x - 3 y

; then A in terms of

m

n

A = \sqrt{\frac{m^{5}}{n^{3}}}

.

{log}_{3} m = x

{log}_{3} n = y

3^{1 - 2 y + 3 x}

can be expressed in terms of

m

n

\frac{3 m^{3}}{n^{2}}

If true then write 1 and if false then write 0.

{log}_{3} m = x

{log}_{3} n = y

3^{2 x - 3}

is expressed in terms of

m

\frac{m^{2}}{n}

, then the value of

n

{log}_{3} m = x

{log}_{3} n = y

2 {log}_{3} A = 5 x - 3 y

A = \sqrt{\frac{m^{5}}{n^{3}}}

If true then write 1 and if false then write 0.

2 x = 3 y + \sqrt{2 x^{2} + m}

, express 'm' in terms of x and y.

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